MR Radar - Center for Advanced Imaging Innovation and Research

MR Radar - Center for Advanced Imaging Innovation and Research

MR Radar:
Parallel Radiofrequency Transmission in Principle and Practice
by
Cem Murat Deniz
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Basic Medical Science
Program in Biomedical Imaging
New York University
May, 2012
___________________________
Daniel K. Sodickson, M.D., Ph.D.
___________________________
Yudong Zhu. Ph.D.
UMI Number: 3524145
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Copyright 2012 by ProQuest LLC.
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All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent on the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3524145
Copyright 2012 by ProQuest LLC.
All rights reserved. This edition of the work is protected against
unauthorized copying under Title 17, United States Code.
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
© Cem Murat Deniz
All Rights Reserved 2012
To Nazik
ACKNOWLEDGEMENTS
I arrived in New York City for my Ph.D. studies five years ago on a rainy,
stormy summer day with Nazik. It is hard to believe that I am writing the
acknowledgement section of my dissertation now. When I look back, I feel deep
gratitude to those people who filled this journey with beautiful memories. I would like
to thank all those people for their help, support, guidance and friendship.
I owe my deepest gratitude to my thesis advisors Daniel K. Sodickson and
Yudong Zhu, who have been teachers, colleagues, and more importantly friends to me.
I feel very fortunate to be part of their research team. Working with Dan was an
amazing learning experience. His enthusiasm and continuous encouragement allowed
me to go beyond my horizons. He always welcomed my questions, critiques, ideas and
provided excellent guidance and feedback whenever I needed them. He taught me how
to become an independent researcher. It was extremely encouraging to feel his support
all the time. Yudong's critical thinking provided a model for me in doing research. I
believe the way I approach a scientific question has developed tremendously over the
years I have worked with Yudong. He was always available whenever I needed his
feedback. I would show up at his door to discuss my questions and he would welcome
me without any hesitation.
My Ph.D. journey was mostly fun thanks to those friends with whom I worked,
hung out, and laughed. I cannot find words to thank Leeor Alon who has been a friend,
colleague, and above all a brother to me. I will always remember our sleepless nights
v
in the 7T room. I don't think any other person could put up with the jokes we make all
the time. Thank you, Leeor!
Gene Cho... You are an amazing friend! Thank you for being my primary
search engine, financial consultant, and personal trainer. You were the best roommate
at the conferences. Thanks for the drinks at the rooftop bar, brother!
Ryan Brown... Ryaaaannn... You are a great researcher and friend. It was
always fun to work with you. Thanks for the detailed edits on all my manuscripts. I
will never forget how we figured out the problem with the parallel transmit system in
the hip study. The golden medals we received for our accomplishment were the best
part of it.
I would like to thank Illiyana Atanasova for being so patient and understanding
for all the jokes and teases coming from us, especially me. Thank you Ili, for creating
a sense of community in the room with all your organizations.
I want to thank everyone in room 420: Vishal Patil, Li Feng, Ding Xia, Elan
Grossmann, Manuska Vaidya, Alicia Yang. Room 420 was a nice work environment
thanks to all of you.
I would like to thank my colleagues at CBI, especially Riccardo Lattanzi,
Kellyanne Mcgorty, Graham Wiggins, Ricardo Otazo, Bei Zhang, Daniel Kim, Pippa
Storey, and Assaf Tal. Ricardo Lattanzi, my post doc... It was a pleasure to work with
you. Your sense of humor makes research fun. Kellyanne, thank you for always being
available whenever I had a question during my experiments. I will never forget our
vi
trip to Alberta on your favorite type of plane. I am grateful to Graham, for his
assistance with SNR analysis and coil design; Ricardo, for his help with all my linear
algebra and numerical optimization questions; Bei, for all her help with the FDTD
simulations; Daniel Kim, for helping me to start on parallel transmit experiments and
sequence design; Pippa for answering all my 'interesting' MR related questions; and
Assaf, for the discussions about adiabatic pulses.
I would like to thank the collaborators from Siemens: Hans-Peter Fautz, Ulrich
Fontius, Bernd Stoeckel, and Niels Oesingmann. I am grateful to Hans-Peter for
providing me with the flip angle sequence and all the support I needed during
experiments. Ulrich was extremely helpful with parallel transmit system hardware and
operations. Niels helped me grasp the details of the sequence design using Siemens
idea environment. Bernd assisted me in solving the problems I had with the MRI
system.
I would like to thank my thesis committee, Elfar Adalsteinsson, Leslie
Greengard, Jens Jensen, and Daniel Turnbull for their precious time and invaluable
feedback. Their questions and comments improved the quality of my work.
Above all, I would like to thank my family, my wife Nazik Dinctopal-Deniz
and my parents Huriye and Duran Deniz. I cannot find the words to thank my
beautiful wife for all her support and encouragement during this journey. She has been
extremely understanding about my work schedule. It was nice to have two Ph.D.
students in the same house. She is the source of joy in my life. I am grateful to my
vii
parents for always being supportive of me. They have always trusted me and my
decisions. I am the person I am today thanks to them.
The last but not the least, I want to thank Joel Oppenheim. I still remember his
warm welcome events at NYU.
viii
ABSTRACT
Magnetic resonance imaging (MRI) has been driven towards high magnetic
fields in order to benefit from correspondingly high signal-to-noise ratio and spectral
resolution. However, technological challenges associated with high magnetic field
strength, such as increase in radiofrequency (RF) energy deposition and RF excitation
inhomogeneity, limit realization of the full potential of these benefits. Parallel RF
transmission enables decreases in RF energy deposition and in the inhomogeneity of
RF excitations by using multiple-transmit RF coils driven independently and operating
simultaneously. In this work, the behavior of RF excitation and RF energy deposition
is explored from an MRI system perspective. New parallel RF excitation techniques
are introduced to measure subject-specific electric field interactions between transmit
elements. These new techniques are demonstrated in phantom and in vivo studies, and
are shown to enable decreases in RF energy deposition while maintaining RF
excitation fidelity. Since the capacity of MRI systems for RF power delivery and
handling are subject to both technological and regulatory limits, a method was
developed to predict the RF power consequence of transmission on each individual
channel during parallel RF transmission, and this method was used to design parallel
transmission RF pulses obeying strict technical and safety limits. Additionally, MRI
system-subject interactions during parallel RF transmission were studied as a function
of the distance between the subject and the transmit RF coils. Lastly, inner-volume RF
excitations were demonstrated as one of the promising potential applications of
ix
parallel RF transmission. In summary, this work represents a step forward in
overcoming technical challenges to demonstrate potential applications of high field
MRI with parallel RF transmission.
x
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
v ABSTRACT
ix LIST OF FIGURES
xii LIST OF TABLES
xiv INTRODUCTION
1 CHAPTER 1: Specific Absorption Rate Benefits of Including Measured Electric Field
Interactions in Parallel Excitation Pulse Design
13 CHAPTER 2: Maximum Efficiency RF Shimming: Theory and Initial Application for
Hip Imaging at 7 Tesla
48 CHAPTER 3: Subject-specific Proactive Management of Parallel RF Transmission 81 CHAPTER 4: RF Energy Deposition and RF Power Requirements in Parallel
Transmission with Increasing Distance from the Coil to the Sample
95 CHAPTER 5: Sparse Parallel Transmit Excitation Trajectory Design for Rapid
Inner-Volume Excitation
107 CONCLUSION
136 APPENDIX
140 REFERENCES
152 xi
LIST OF FIGURES
Figure 1.1 FDTD simulation setup. .............................................................................. 20 Figure 1.2 Excitation k-space and desired profile. ....................................................... 26 Figure 1.3 Phantom experiment setup. ......................................................................... 29 Figure 1.4 Additional inputs used in pulse design for the phantom experiments. ....... 31 Figure 1.5 Global SAR when the power correlation matrix is incorporated into parallel
RF pulse design. ........................................................................................................... 36 Figure 1.6 Experimental results. ................................................................................... 39 Figure 1.7 RF pulse waveforms and RF net power ...................................................... 41 Figure 2.1 Experimental setup. ..................................................................................... 57 Figure 2.2 Steps required for the calculation of the maximum efficiency RF shimming
weights. ......................................................................................................................... 63 Figure 2.3 Representative axial GRE images of one volunteer at 7 T ......................... 68 Figure 2.4 Adiabatic half passage RF pulse results ...................................................... 70 Figure 2.5 SNR comparison at 3 T and 7 T .................................................................. 76 Figure 3.1 Example of calibrated power correlation matrices. .................................... 88 Figure 3.2 Desired excitation profile and k-space trajectory ....................................... 88 Figure 3.3 Bloch simulation results and axial GRE images of designed RF pulses .... 90 Figure 3.4 Comparison of individual channel actual power measurements ................. 91 Figure 3.5 Measured power for RF pulses designed with different power constraints.94 Figure 4.1 Transmit array geometries for spherical simulations. ................................. 99 xii
Figure 4.2 Transmit array geometries for cylindrical simulations. ............................ 100 Figure 4.3 Optimized global SAR and RF power requirements versus lift-off.......... 102 Figure 4.4 Local SAR vs lift-off for the sphere.......................................................... 105 Figure 4.5 Optimized global SAR and RF power requirements versus lift-off for the
cylinder. ...................................................................................................................... 106 Figure 5.1 Schematic illustration of how selectivity in the image domain depends upon
the dimension of excitation k-space. .......................................................................... 114 Figure 5.2 An example of 2D spiral RF pulse design. ............................................... 116 Figure 5.3 Various k-space trajectories which are used for 3D selective RF excitation
using one transmit channel. ........................................................................................ 118 Figure 5.4 B1+ distribution of the individual elements. .............................................. 127 Figure 5.5 Distribution of the selected k-space locations for both algorithms. .......... 129 Figure 5.6 Designed k-space trajectories .................................................................... 131 Figure 5.7 Experimental flip angle profiles of designed LTA RF pulses .................. 131 Figure 5.8 Axial and sagittal GRE images acquired .................................................. 132 Figure A.1 Workflow of an RF shimming experiment. ............................................. 145 Figure A.2 Screenshot of RF Shimming GUI ............................................................ 146 Figure A.3 Workflow of a parallel transmission experiment. .................................... 150 Figure A.4 Screenshot of Parallel Transmit GUI ....................................................... 151 xiii
LIST OF TABLES
Table 0.1 Temperature limits in MR experiments.......................................................... 4 Table 0.2 SAR limits for local transmit coils ................................................................. 4 Table 1.1 Comparison of STA parallel RF pulse behavior in a simulation ................. 37 Table 1.2 Experimental parallel RF pulse behavior ..................................................... 43 Table 2.1 Comparison of four RF shimming methods ................................................. 71 Table 2.2 Experimentally measured net power deposition and corresponding flip angle
...................................................................................................................................... 72 Table 2.3 Calculated maximum efficiency RF shimming weights .............................. 73 Table 2.4 SNR results in the hip articular cartilage of the volunteers at 3 T and 7 T. . 75 Table 3.1 Power comparison of RF pulses with different power constraints. .............. 93 xiv
INTRODUCTION
Among today's large variety of medical imaging techniques, Magnetic
Resonance Imaging (MRI) differentiates itself by its non-invasive nature and its soft
tissue contrast, which facilitates diagnostic imaging of the brain, heart, muscles and
many other organs or tissues. MRI is based on the physical phenomenon called
Nuclear Magnetic Resonance (NMR) which was first detected in solid materials
independently by Purcell et al. (1) and Bloch (2) in 1946 after its discovery in gases by
Rabi et al. (3) in 1938. The significant step from NMR that renders MRI experiments
possible was discovered by Lauterbur (4) in 1973. Lauterbur achieved spatial
encoding of the MR signal by superimposing additional magnetic field gradients on
the main magnetic field, thereby enabling the exact position of the NMR signal in the
sample to be decoded and an image to be formed. Based on Laterbur’s gradient
encoding approach, Kumar et al. (5) proposed Fourier imaging in 1975, which formed
the basis of most variants of MRI that are currently in use. However, Fourier imaging
with gradient encoding implied a fundamental restriction on the speed of MRI
acquisition, since only one position in the gradient encoded spatial frequency space
(which was later defined as k-space by Twieg (6) and Ljunggren (7)) could be sampled
at a time.
The speed of MRI acquisition has increased dramatically with improvements
in gradient technology and the development of new fast imaging acquisition
techniques, such as echo-planar imaging (8), turbo spin echo (9) and spiral imaging
1
(10). However, the sequential nature of Fourier encoding was still one of the main
limitations on the achievable speed. The concept of using multiple receivers for the
purpose of scan time reduction in Fourier imaging was suggested in 1988 (11).
However, successful experiments using parallel receivers for the purpose of scan time
reduction were not demonstrated until the introduction of parallel magnetic resonance
imaging methods in the late 1990s (12,13). The advent of parallel MRI opened a wide
area of research into the acceleration of MR scanning through undersampling of
k-space and subsequent reconstruction of missing image information using
complementary information from the elements of radiofrequency (RF) coil arrays.
Numerous parallel imaging reconstruction techniques and strategies have been
developed since then (14-18) and parallel MRI has become a well established
technique widely used in clinical MRI. Despite the advantage of faster scanning with
parallel MRI, loss of signal-to-noise ratio (SNR) in the reconstructed images (as
compared with fully gradient-encoded images using the same coil array) was observed
due to reduced time averaging of noise using fewer k-space samples as well as to noise
amplification in the image reconstruction process.
Since the SNR of the magnetic resonance signal is known to scale up with
increasing main magnetic field strength (B0) (19), the history of MRI has also seen a
progressive increase in field strength, with the emergence in the past decade or so of
ultra-high-field (UHF, ≥ 7 Tesla (T)) MRI systems for human use. High SNR can be
used to improve spatial / temporal resolution for improved image quality and to
2
decrease image acquisition times. However, the practical SNR increase enabled by
UHF-MRI is substantially limited by constraints on the specific absorption rate (SAR),
a measure of RF energy deposition in tissue. SAR is directly related to electric field
(E) inside the subject. In MRI, E field inside the subject is induced by the RF
magnetic field (B1) which interacts with spins and induces MR signal. This
concomitant E field deposits RF energy in the imaged body and determines SAR,
which is subject to regulatory limits (20,21) aimed at preventing unacceptable
temperature increases within the human body. Allowed values for temperature rise of
the patient caused by MR scanner are defined by the International Electrotechnical
Commission (IEC) as shown in Table 0.1. MR scanners are operated in three various
operating modes as can be seen from Table 0.1. Default operating mode of MR
scanner is the normal mode which guarantees that RF power deposition cannot cause a
physiological stress to patients. Other two operating modes can cause physiological
stress to patients and they have to be controlled by medical supervision. Compliance
to the temperature rise limits for local transmit coils can be achieved by limiting the
SAR (Table 0.2), which is derived so that the spatially localized temperatures are not
expected to result in tissue damage.
3
Table 0.1 Temperature limits in MR experiments (Table 201.104 from Ref. (21))
Operating
Maximum Core
Maximum Local
Rise of Core
Mode
Temperature
Tissue Temperature
Temperature °C
Normal
39
39
0.5
First Level
40
40
1
>40
>40
>1
Controlled
Second Level
Controlled
Table 0.2 SAR limits for local transmit coils (Table 201.106 from Ref. (21))
Averaging Time
6 min
Local SAR
Body Region
Head
Trunk
Extremities
Operating Time
(W/kg)
(W/kg)
(W/kg)
Normal
10 a
10
20
First Level
>20 a
20
40
>20 a
>20
>40
Controlled
Second Level
Controlled
Short Duration
SAR
a
The SAR limits over any 10 s period shall not exceed two times the
stated values
NOTE In cases where the orbit is in the field of a small local RF transmit coil, care should be
taken to ensure that the temperature rise is limited to 1°C
4
As the B0 field strength increases, the magnitude of E field per unit flip angle
increases (19) and safety limits on allowed SAR limit achievable SNR. Additionally,
at UHF, the interaction of the electromagnetic (EM) field with dielectric tissues tends
to exacerbate inhomogeneities in RF power deposition, which may result in dangerous
local hot-spots. In addition to the SAR limitations, inhomogeneity of the appropriately
polarized transverse magnetic field B1+ hampers clinical use of UHF-MRI systems.
This RF inhomogeneity is related to the reduction in RF wavelength at high field and
causes inhomogeneities of the image contrast and SNR, which can diminish the
quality and diagnostic value of MR images.
In order to overcome patient-induced inhomogeneous RF excitation at UHF,
several RF excitation methods have been proposed using multiple RF transmit coils.
The first method was RF shimming (19,22,23), in which multi-element transmit coil
arrays are driven with a single RF waveform by adjusting phase and amplitude in
individual coils independently. This technique has been successful in improving the
B1+ homogeneity in excited volumes, especially in small local regions-of-interest
(ROIs) (24,25). However, the efficiency of RF shimming diminishes as the ROI
becomes larger. Thus, new approaches have been introduced to mitigate B1+
inhomogeneities in large ROIs. For example, various tailored excitation k-space
trajectories (26,27) have been utilized, and have been shown to reduce B1+
inhomogeneity. Later, parallel RF excitation techniques (28,29) combined and
5
extended the benefits of these two approaches. Parallel excitation methods have been
used to compensate for patient-induced RF inhomogeneities at high B0. In parallel RF
excitation, individual elements of multi-element transmit coils are driven
simultaneously with distinct tailored RF pulses sharing a common gradient waveform.
The additional degrees of freedom available in parallel RF excitation pulses can be
used to shorten multidimensional pulses (30,31), improve spatial definition of the
excitation pattern (32) and decrease RF power deposition (29).
Even though the parallel RF excitation offers a means of overcoming technical
problems associated with UHF, the technical development stage of parallel RF
excitation has been slow compared to that experienced in the field parallel MR
reception. The potential of parallel RF excitation has not been fully explored in human
studies due to the complexity and cost of additional equipment required, the
computational complexity of designing RF pulses, especially for large-tip-angle
(LTA) pulses, and importantly, the need for a real time SAR assessment to ensure
patient safety. The requirement of an additional RF pulse synthesizer and amplifier for
each transmit channel increases the cost of parallel transmit equipment as the number
of transmit channels increases. The cost of parallel RF transmit systems is expected to
decrease in the future as add-on prototype systems are replaced with fully integrated
ones. Since the introduction of the first parallel RF excitation pulse designs (28,29),
various new approaches to the design of parallel excitation RF pulses with reduced
computational complexity have been proposed, first for small-tip-angle (STA) (30,32-
6
39) and later for LTA (40-42). Although the developments in parallel RF excitation
pulse design have been shown to mitigate B1+ inhomogeneity effectively and enable
application specific tailored excitation profiles, the usage of parallel RF excitation is
still limited to the STA regime in subjects (43-45) due to concerns about SAR.
The SAR behavior of parallel excitation RF pulses has been studied
extensively using a variety of excitation k-space trajectories (46-48), coil designs
(49,50), acceleration factors (51), and RF pulse design formalisms (29,36,52-54).
Evaluation and prediction of SAR consequences of designed parallel RF excitation
pulses have commonly relied upon EM simulations using virtual human body models
(55,56) due to a lack of accurate means of measuring and predicting concomitant E
fields inside the human body. Recently, the use of pre-scan-based individualized body
models (57,58) have begun to be used in the EM simulations in order to estimate SAR
closely. However, it remains unclear whether it will be feasible to adapt the details of
simulated coil-subject setup in order to closely track what is happening or what will
happen to a subject during scan. For instance, concerns about using pre-scan-based
virtual body models and EM simulations to estimate actual SAR have been motivated
by the observation of significant SAR changes resulting from minor variations in body
model (59). In order to overcome these concerns, pre-scan-based SAR calibration
methods have been proposed (60-63). These methods enable accurate SAR predictions
specific to coil-subject setup and do not require assumptions about the subject or the
scanner setup. In addition to SAR prediction capability, an additional layer of system
7
monitoring in the parallel RF excitation chain has been implemented to ensure subject
safety, using either pick-up coils (64) or directional couplers (65,66). These additional
monitoring systems have been shown to detect system changes such as hardware
failure, system instability and patient position change which were undetectable with
previous RF monitoring systems.
Apart from SAR considerations, another emerging area of research in parallel
RF excitation involves the use of transmit array to shorten multidimensional RF
pulses, e.g. for tailored regional excitations. For instance, by using accelerated
multidimensional RF pulses, inner-volume excitations with high spatial selectivity
have been experimentally realized (31,67,68). Inner-volume excitation is expected to
reduce total signal acquisition time by reducing the extent of the required receive
FOV. Additionally, smaller inner-volume excitations tend to result in lower SAR for
small acceleration factors (51), which increases the importance of inner-volume
excitations at UHF.
In the light of all these developments, parallel RF excitation, with appropriate
SAR prediction and monitoring, is likely to continue to play an important role in the
future of MRI by the improving diagnostic value of UHF-MRI.
Research Problem Statement
Parallel RF excitation offers the flexibility to tailor both E field and B field
simultaneously. This thesis work centers around the general goal of achieving a
favorable balance between magnetic and electric fields for high-performance MRI.
8
Various approaches to increasing / tailoring B1+ field while decreasing E field in the
body are described.
First, we show how to use measurable subject-specific E field interactions of
individual transmit elements in order to decrease global SAR while achieving a target
B field distribution with high fidelity. The new concept of subject-specific SAR
prediction based on the measurable E field interactions is shown to facilitate the
subject-specific tailoring of B1+ profiles while managing global SAR.
Even though fully functional parallel RF excitation systems have been installed
worldwide, the majority of in vivo research on these systems to date has focused on
RF shimming due to its reduced computational and operational complexity as
compared to full parallel RF excitation. In this arena, we use subject-specific SAR
prediction to develop a maximum efficiency RF shimming method. This new RF
shimming approach aims to obtain the lowest possible net radiofrequency power
deposition into the subject for a given transverse magnetic field strength and
guarantees the global optimality of the resulting RF shimming coefficients.
As parallel excitation relies on simultaneous RF excitation from multiple coil
elements, interactions and coupling between coil elements and between coils and body
structures become more important than for single-element transmit systems. We show
how to extend the subject-specific global SAR prediction and monitoring method to
predict individual channel forward and reflected power for any RF excitation. By
9
using this new prediction capability, we design parallel excitation RF pulses meeting
strict MR scanner power handling limits.
The role of coil array geometry is well studied for parallel MR reception. In
this thesis we investigate the role of coil geometry on SAR and power requirements in
parallel RF excitation. As an example, we change the distance between coil array and
subject and investigate the SAR and power requirements as a function of the distance
between coil array and subject.
Parallel RF excitation offers the flexibility to decrease the RF pulse length by
undersampling excitation k-space trajectories. Shorter RF pulses are especially crucial
for multidimensional RF excitation, where the RF pulses tend to be longer than for
traditional (e.g. slice- or slab-selective) excitation. In this thesis we propose a method
that enables shorter multidimensional RF pulses for inner-volume excitation by sparse
selection of excitation k-space locations to be traversed. The method enables
excitation k-space accelerations beyond the limits of traditional parallel RF excitation
which is limited by the number of transmit coil elements.
Thesis Outline
This thesis consists of the introduction, five chapters describing each of the
research areas outlined above, a final conclusion and an appendix. The next chapter
(Chapter 1) is adapted from a manuscript published in the journal Magnetic Resonance
in Medicine and it explores the effects upon SAR of incorporating experimentally
measurable E field interactions into parallel RF transmission pulse design. Numerical
10
simulations and phantom experiments were used to demonstrate SAR reductions in
new RF pulse design strategy during parallel RF transmission while obtaining similar
excitation fidelity. Additionally, measured E field interactions were used to predict the
net RF power deposition of any parallel RF excitation pulse.
Chapter 2 is an extended version of an abstract presented in 2011 ISMRM
workshop on ultra-high field systems and applications at Lake Louise. It proposes a
new RF shimming algorithm, i.e. maximum efficiency RF shimming, which seeks to
obtain the lowest possible net radiofrequency power deposition into the subject for a
given transverse magnetic field strength. Experiments with volunteers were used to
demonstrate practicability of maximum efficiency RF shimming. Additionally,
quantitative SNR comparison of 3 T and 7 T imaging in the hip articular cartilage was
performed.
Chapter 3 investigates parallel RF excitation from an MR system perspective.
It describes the subject-specific proactive management of parallel RF excitation
aiming to obey RF power requirements of the hardware and SAR requirements for the
subject. Phantom experiments were used to compare RF pulses with and without
subject-specific power supervision.
Chapter 4 is an extended version of an abstract presented in 2009 at the
seventeenth annual meeting of the ISMRM in Hawaii. It investigates the SAR
behavior and the power requirements of parallel RF transmission as the distance
between transmit elements and the surface of the object is altered. Using numerical
11
simulations, various geometrical arrangements of coil elements around a cylindrical
and a spherical object are explored.
Chapter 5 is an extended version of an abstract presented in 2011 at the
nineteenth annual meeting of the ISMRM in Montreal. The chapter summarizes the
excitation k-space concept and the requirements for choice of an excitation k-space
trajectory. Sparse selection of the excitation k-space trajectory is demonstrated,
enabling inner-volume excitations with a UHF whole-body human scanner.
The concluding chapter summarizes the main topics discussed in the thesis and
outlines possible future work.
The appendix demonstrates graphical user interfaces (GUIs) developed in the
course of this work in order to increase the efficiency and the accuracy of parallel
transmit experiments. Workflows are explained with overlying screen captures of two
GUIs: one for RF shimming and one for fully parallel RF transmission pulse design.
12
CHAPTER 1: Specific Absorption Rate Benefits of Including Measured Electric
Field Interactions in Parallel Excitation Pulse Design
Deniz CM, Alon L, Brown R, Sodickson DK, and Zhu Y
Specific Absorption Rate Benefits of Including Measured Electric Field Interactions in
Parallel Excitation Pulse Design
Magnetic Resonance in Medicine 2012 (67): 164-174
Author contributions:
Cem Murat Deniz: Manuscript draft, study design, RF pulse design, sequence design,
data acquisition, data interpretation, literature research
Leeor Alon: FDTD simulations, power calibration system and software, manuscript
editing
Ryan Brown: MR coils and interface, manuscript editing
Daniel K. Sodickson: Study concept, manuscript editing
Yudong Zhu: Study concept, data interpretation, manuscript editing
13
Peer reviewed abstracts from the chapter:
Deniz CM, ALon L, Brown R, Fautz H-P, Sodickson DK, and Zhu Y
Parallel RF Pulse Design with Subject-Specific Global SAR Supervision
In Proceedings of the 19th Scientific Meeting, International Society for Magnetic
Resonance in Medicine, Montreal, Canada. page 210, 2011.
Deniz CM, ALon L, Brown R, Fautz H-P, Sodickson DK, and Zhu Y
Real Time RF Power Prediction of Parallel Transmission RF Pulse Design at 7T
In Proceedings of the 18th Scientific Meeting, International Society for Magnetic
Resonance in Medicine, Stockholm, Sweden. page 1454, 2010
Deniz CM, Alon L, Lattanzi R, Sodickson DK, and Zhu Y
SAR Benefits of Including E-Field Interactions in Parallel RF Pulse Design
In Proceedings of the 18th Scientific Meeting, International Society for Magnetic
Resonance in Medicine, Stockholm, Sweden. page 4930, 2010.
14
1.1 Abstract
Specific absorption rate management and excitation fidelity are key aspects of
radio frequency pulse design for parallel transmission at ultra high magnetic field
strength. The design of radio frequency pulses for multiple channels is often based on
the solution of regularized least squares optimization problems for which a
regularization term is typically selected to control the integrated or peak pulse
waveform amplitude. Unlike for single channel transmission, the specific absorption
rate of parallel transmission is significantly influenced by interferences between the
electric fields associated with the individual transmission elements, which a
conventional regularization term does not take into account. This work explores the
effects upon specific absorption rate of incorporating experimentally measurable
electric field interactions into parallel transmission pulse design. Results of numerical
simulations and phantom experiments show that the global specific absorption rate
during parallel transmission decreases when electric field interactions are incorporated
into pulse design optimization. The results also show that knowledge of electric field
interactions enables robust prediction of the net power delivered to the sample or
subject by parallel radio frequency pulses before they are played out on a scanner.
1.2 Introduction
Multidimensional spatially selective excitation pulses are used to tailor
volumetric spin excitation (69). Volumetric spin manipulations can serve as a tool to
reduce susceptibility artifacts (70), to improve spatial resolution via inner volume
15
selection (71), and, especially at high magnetic field strength, to compensate for radio
frequency (RF) field inhomogeneity (27). However, RF pulse durations are generally
on the order of transverse magnetization decay ( T 2* ) which limits the practical
application of multidimensional excitations.
Parallel excitation using multiple transmit channels (28,29) has been shown to
allow significant acceleration of multidimensional RF pulses, bringing them within
range of practical applications. There are representative methods for the design of
accelerated multidimensional spatially selective RF pulses in the literature (28,29,34).
However, reduction in RF pulse length often results in increased power deposition in
tissue (72), defined as specific absorption rate (SAR).
SAR behavior in parallel RF transmission was first addressed by Zhu (29),
who proposed a pulse optimization approach in which the degrees of freedom
available in parallel transmission are used not only to achieve a target excitation
profile but also to minimize SAR, expressed as a quadratic function involving the RF
pulse waveforms and a characterization of electric field-induced RF loss. In the
absence of experimental knowledge of transmit coil electric fields, simulations have
been used to analyze / improve the SAR behavior of RF pulses with a variety of
excitation k-space trajectories (46,47,73), coil designs (49,50) acceleration factors
(51) and alternative optimization formalisms (36,74). Recently, an in vivo SAR
calibration method (60) for parallel RF transmission was introduced which enables
direct measurement of the electric field correlations required for accurate SAR
16
prediction and control. With this method, measurements of forward and reflected
power corresponding to a set of predefined parallel RF pulses are used to estimate the
power correlation matrix in a rapid and subject-specific manner. This correlation
matrix may then be used to predict the true RF energy delivered to the imaged sample
or body by any set of parallel pulses, without reliance on simulations or other
assumptions about body geometry, tissue properties, or the coil system.
This work represents an initial effort to incorporate a truly subject-specific
SAR prediction model, made possible by the experimentally calibrated power
correlation matrix, directly into parallel RF transmission pulse design. In this work,
regularization-based methods proposed by Grissom et al. (34) and Xu et al. (40) were
modified to capture global SAR behavior with a new regularization term for small and
large tip angle regimes, respectively. Furthermore, the use of the calibrated power
correlation matrix inside a regularization term extends the SAR-optimal parallel RF
pulse design approach proposed by Zhu (29) for echo-planar excitation k-space
trajectories to arbitrary trajectories and large flip angles.
Simulations of various coil-sample configurations with distinct power
correlation characteristics were used to evaluate the effects on global SAR realized by
employing the power correlation matrix in RF pulse design. These results were
compared to those obtained with RF pulses designed using the conventional integrated
regularization that disregards electric field interactions. Experimental investigations
were further conducted to investigate the feasibility of subject-specific global SAR
17
prediction and proactive management. This involved the use of both the calibration
system (60,61) for measuring the power correlation matrix and the present method that
accounts for electric field interference effects in parallel RF pulse design. Finally,
global SAR predictions were compared to actual power measurements in example
cases of conventional and proposed SAR-optimized RF pulse designs.
1.3 Materials and Methods
1.3.1 Electromagnetic Simulations
Numerical simulations were used to analyze SAR generated from parallel RF
pulses with and without electric field interactions incorporated in the pulse design. The
electric and magnetic fields of four-element transmit array were simulated using the
finite difference time domain method (xFDTD 6.3, REMCOM, State College, PA) at 7
T (297.2 MHz), using mesh data representing both a homogeneous rectangular water
phantom and a human body model.
Three different coil array configurations and relative element positions with
respect to the imaged objects are illustrated in Figure 1.1. Four identical square array
elements with 7 cm length were placed 1 cm above the object or body surface. In two
configurations (Figure 1.1a,b), coils were partially overlapped to imitate a common
practice to reduce inductive coil coupling, although inductive coupling was not present
in these simulations. Overlapping of the elements was achieved without artificial
short-circuits by offsetting the elements slightly with respect to each other in a
direction perpendicular to the plane of the coils. The simulated rectangular water
18
phantom had dimensions 24 x 20 x 24 cm3 and a uniform conductivity, σ, of 0.6 S / m
and relative permittivity, εr, of 80. The simulated HUGO human body model (Figure
1.1d) had heterogeneous dielectric properties and tissue density. Both objects were
defined on a grid of 5 x 5 x 5 mm3 voxel size. Each array element was driven by an
ideal 1-ampere current while keeping the other elements dormant (and therefore
eliminating inductive coupling between transmit elements). Steady-state electric
fields, El(r) (V / m / A), and magnetic fields, Bl(r) (T / A), for each transmit element,
l, were computed for all spatial locations, r, inside the object. The transmit sensitivity
map of the lth element, Sl(r), was calculated as Sl(r) = B1+,l(r) = (Bl,x(r) + i Bl,y(r)) / 2
(75). Figure 1.1e,f shows the phase (e) and amplitude (f) of the B1+ field of all coils in
setup C for the water phantom.
19
Figure 1.1 FDTD simulation setup. Setup A, B and C represent different coil configurations
which are used on a water block phantom (a, b, c) and a human mesh (d). e and f show the
phase and the magnitude of the B1+ map for setup C in the water phantom.
1.3.2 Global Specific Absorption Rate Calculations
RF power deposition into the object can be calculated with knowledge of the
unit-drive steady state electric fields of all transmit elements as well as the electrical
properties of the object and the designed pulse waveforms. Power deposition, P, of
parallel transmit arrays at location r and at each time instant pΔt can be calculated as:
20
P (r , pt ) 
 (r )
2
E (r , p  t )
2
2
[1.1]
L
where σ is the electrical conductivity, E(r, pt )   bl ( pt )el (r ) is the superposition
l 1
of the unit-current electric fields el of the L transmit elements multiplied by the
driving RF pulse waveforms bl, and p is an integer index indicating time in multiples
of the waveform sampling interval
t . As shown in Refs. (29,72), total RF power
deposition into the object at any time instant pΔt can be calculated by taking the
following volume integral over the object:
 ( pt )   P(r, pt )dv  b Hpt Φb pt
[1.2]
V
T
where b pt  b1, pt  b L , pt  is the concatenation of the RF pulse waveforms,
denotes the matrix transpose,
H
T
denotes the complex conjugate transpose, and Φ
defining the L x L positive definite Hermitian power correlation matrix with (i, j)-th
element is given by:
i , j 
1
 (r )E*i (r, pt )  E j (r, pt )dv

2V
[1.3]
where * indicates complex conjugation. Global SAR (W / kg) can be calculated as the
average total RF power deposition into the object divided by the object mass m:
 
1
mT
Nt 1
 t ( pt )
p 0
where Nt is the number of time samples and T is the RF pulse length.
21
[1.4]
1.3.3 Parallel Excitation RF Pulse Design
The spatial domain parallel RF pulse design method (34) and linear class largetip-angle (LCLTA) method (40) were used to design small-tip-angle (STA) and largetip-angle (LTA) RF pulses, respectively.
Using the linearization of the Bloch equations within the STA regime (69) and
neglecting relaxation terms, the transverse magnetization M (r, T ) produced by the
parallel RF pulse at position r and time T can be expressed as:
L
T
l 1
0
M (r, T )  i M 0 (r ) Sl (r)  bl (t )eiB0 (r )(t T ) eirk (t ) dt
where
[1.5]
 is the gyromagnetic ratio, M0(r) is the equilibrium magnetization at spatial
position r, L is the number of transmit coils with sensitivity patterns Sl(r), ΔB0(r) is the
local off-resonance field map, bl(t) is the RF pulse waveform of coil l, and
T
k (t )    G ( )d is the excitation k-space trajectory, defined as the time reversed
t
integration of the gradient waveforms G( ) (69). By discretizing in time to Nt samples
and in space to Ns positions, and concatenating matrices and vectors in Eq. [1.5] along
the coil dimension, as in Grissom, et al. (34), RF pulses for parallel excitation can be
calculated to produce a desired transverse magnetization profile vector mdes using a
selected k-space trajectory by solving:
2
bˆ full  arg min{ A fullbfull  m des 2  R(bfull )}
bfull
22
[1.6]
where Afull   A1  AL  in which Al is a Ns x Nt system matrix with elements
aij  itM 0  ri  Sl  ri  e
iB0 ( ri )( t j T ) iri k ( t j )
e
, b full  b1  b L  is a concatenation of the
T
RF pulse waveforms of L coils and R(bfull) is a general parameter for regularization
term which will be explained in detail at the end of this section.
When "linear class" assumptions (76) about excitation k-space are satisfied and
relaxation effects are neglected, the flip angle distribution,  (r) , of parallel RF pulses
in the LTA regime may be expressed, following Xu et al. (40), as:
L
T
 (r )    S (r )  bl* (t )eiB (r )(t T ) eirk (t ) dt
l 1
*
l
[1.7]
0
0
By discretizing in time and space and concatenating matrices and vectors,
Eq. [1.7] can be expressed in matrix form as θ  Cfullb*full , where Cfull  C1  CL  ,
and Cl is a Ns x Nt system matrix with elements cij  tSl* (r j )e
 iB0 ( ri )( t j T )  iri k ( t j )
e
.
Given a desired flip angle distribution, θdes, and a chosen k-space trajectory, parallel
pulse waveforms can be calculated by solving the minimization problem:
2
bˆ full  arg min{ Cfullb*full  θdes  R(b*full )}
2
b*full
[1.8]
Regularization terms R in both STA (Eq. [1.6]) and LTA (Eq. [1.8]) designs
can be used to protect against an ill-conditioned matrix inversion and to control the
integrated or peak RF pulse waveform. One widely used approach in RF pulse design
H
is Tikhonov regularization R (b full )   b full
b full , where β is used to tradeoff excitation
23
profile error against the integrated RF pulse waveform amplitude square (34,40,77).
Unlike in single-channel transmission systems, however, controlling the integrated RF
pulse waveform amplitude may not be an effective way to minimize SAR in parallel
pulse design, where SAR may be significantly influenced by electric field interactions
inside the object (29). We propose to use the following regularization term in STA RF
pulse design which incorporates the full constructive and destructive electric field
interferences into RF pulse design that are ignored by conventional regularization
terms:
H
RSTA (bfull )   bfull
Φfullbfull
[1.9]
In Eq. [1.9],
Φfull
0
Φ





 0
Φ  N LxN L
t
[1.10]
t
where Φ is the power correlation matrix defined in Eq. [1.3], and the β parameter is
now used to trade off excitation error against true global SAR. Similarly, the
regularization term for LCLTA RF pulse design can be defined as:
H
RLCLTA (bfull )   bfull
Φ*fullbfull
[1.11]
Eqs. [1.6] and [1.8], now with the revised regularization terms, can be efficiently
solved with conjugate gradient methods.
24
1.3.4 RF Shimming
As a special case of parallel RF transmission, the RF shimming method (19,23)
can be used to correct B1+ inhomogeneities by time-independent control of relative
amplitude and phase of individual transmit elements which share a common RF
waveform. The desired B1+ distribution Sdes, is generated by applying a set of complex
weights, wl, to the individual transmit elements such that the following equality holds
at every spatial location r inside the selected shim volume:
L
Sdes (r)   wl Sl (r)
[1.12]
l 1
By discretizing spatial locations once again into Ns samples, Eq. [1.12] can be
written in the matrix form:
 Sdes (r1 )   S1 (r1 ) S 2 (r1 )  S L (r1 )   w1 
 S (r )   S (r ) S (r )  S (r )   w 
2 2
L 2  2
 des 2    1 2
    


   

 
 
(rs )  S L (rs )   wL 
des (rs ) 
 S
 S1 (rs ) S2 


 
 
w
S des
S
[1.13]
Regularized least-squares solution for the desired RF shim coefficients can be
efficiently obtained by solving:
2
ˆ  arg min{ Sw  S des 2  R(w )}
w
[1.14]
w
where R(w) is the regularization term which can be defined either as R (w )   w H w
(penalizing waveform amplification) or as R (w )   w H Φw (penalizing true global
SAR directly) following the discussion in the previous section.
25
1.3.5 Simulated RF Pulse Designs
A constant density inward spiral trajectory (Figure 1.2a) was used to cover
excitation k-space for simulated pulse designs, using the following gradient design
parameters: maximum amplitude 40 mT / m, maximum slew rate = 150 mT / m / s,
and sampling period = 10 μs. The k-space trajectory was chosen to achieve a spatial
resolution of 10 mm. 12 spiral turns were used for the unaccelerated pulse trajectory,
and acceleration by a factor of R was achieved by undersampling radially, yielding
12/R turns. Based on the parameters listed above, RF pulse lengths of 5 ms for R = 1
and 2.5 ms for R = 2 were in effect.
Figure 1.2 Excitation k-space and desired profile. a: Constant density spiral-in excitation
k-space trajectory used in simulations (acceleration factor R = 1). b: Desired excitation profile.
c, d: Bloch equation simulation results for RF pulses designed with conventional (c) and
proposed (d) methods for setup C.
26
2D transmit sensitivity maps of 5 mm resolution for all transmit elements were
extracted from 3D FDTD simulations after defining the slice of interest (1.5 cm and 4
cm below the surface for water phantom and virtual human mesh, respectively). For
RF shimming simulations, a desired coronal B1+ distribution, Sdes, with uniform
magnitude and zero phase inside the water phantom was selected. For parallel RF
pulse design, the desired excitation profile for the water phantom (Figure 1.2b) was
defined as a centrally located coronal disk of uniform flip angle and zero phase with
diameter equaling 15 cm. For the human mesh dataset, a 7.5 x 15 cm2 rectangle of
uniform flip angle and zero phase at the center of FOV was defined as the desired
excitation profile. Flip angles of 10° and 90° were chosen for STA and LTA RF pulse
designs, respectively.
RF pulses and RF shim weights were calculated from Eqs. [1.6], [1.8] and
[1.14] with conventional and proposed regularization terms, using custom code
developed in Matlab (version 7.9, MathWorks, Inc., Natick, MA, USA). Using the
transmit coil sensitivity profiles combined with the computed pulse waveforms / RF
shim weights, the net magnetic fields resulting from the parallel RF pulses / RF shim
weights were calculated. Subsequently, spinor domain-based Bloch equation
simulations
described
in
Ref.
(78)
and
developed
by
Hargreaves
(http://mrsrl.stanford.edu/~brian/blochsim/) were used to generate the excitation
profile of parallel RF pulses over a selected slice with 2.5 x 2.5 mm2 resolution.
Relaxation effects were ignored in Bloch simulations.
27
To quantify excitation fidelity of a pulse design, the normalized
root-mean-square error (NRMSE) between the desired magnetization and the
magnetization profile obtained from Bloch simulation, mbl, was calculated as
mbl  mdes 2 / mdes 2 . For fair comparison of various pulse designs’ SAR
performance, the NRMSE’s of the designs were equalized using distinct heuristically
chosen regularization parameters. Excitation fidelity can be similarly quantified and
aligned for the RF shimming cases. At comparable fidelity, global SAR performance
of RF pulses or RF shim weights designed with different regularization terms were
then compared.
1.3.6 Experimental RF Pulse Designs
To evaluate the benefits of incorporating global SAR information into the RF
pulse design, experiments were performed on a Siemens whole body 7 T Magnetom
scanner (Erlangen, Germany) equipped with an eight-channel parallel transmit system.
An eight-channel stripline coil array was used for RF excitation and reception (Figure
1.3a). The striplines were mounted on an acrylic former with 27.9 cm diameter and
azimuthally separated by 45. The striplines were built on 15 x 4 x 1.3 cm3 teflon bars
with 14 x 2 cm2 conductive strips, 15 x 4 cm2 ground planes, and sidewalls with 1.3
cm height to reduce inter-element coupling. Two tuning capacitors of approximately
6.8 pF and 8.2 pF were inserted on opposing ends of each stripline to achieve
resonance at 297.2 MHz. The striplines were matched to 50 through a series
capacitor of approximately 2.2 pF while loaded with a 7.3-L cylindrical water
28
phantom with 15 cm diameter containing 1.25 g / L NiSO4.6H2O and 4 g / L NaCl
(σ = 0.7 S/m, εr = 80.6) (Figure 1.3b). Forward and reflected power readings of eight
channels at a sampling rate of 10 μs were obtained with a power sensor (NRP-Z11,
Rhode&Schwarz, Munich, Germany) connected to directional couplers at the output
of each RF amplifier via an RF switch (Dual 16 x 1 MUX, National Instruments,
Austin, TX, USA).
Figure 1.3 Phantom experiment setup. a: 8 channel transmit-receive coil array. b: Cylindrical
water phantom. c: B1+ amplitude map for each element of the array. d: B1+ phase map for each
element of the array.
B1+ calibration was performed following the method described in Ref. (79). In
order to obtain individual transmit channel B1+ profiles, non- or selective saturation
pulses on one channel at a time were used to produce a spatial-dependent flip angle
map. A reference image was obtained from selective excitation of all channels without
magnetization preparation. The reference image was used to obtain the cosine of the
29
flip angle map by dividing the saturated image. RF shimming was used to have
enough SNR throughout the reference image. B1+ magnitude maps (Figure 1.3c) in the
axial plane through the isocenter were obtained by processing data from 1.5 ms
rectangular saturation pulses followed by a multishot segmented spoiled turbo fast
low-angle shot (FLASH) imaging acquisition with 2 segments (segment repetition
time = 5 s). Relative B1+ phase distributions for different coils (Figure 1.3d) were
calculated from additional turbo FLASH scans using only one coil for excitation at a
time. The following imaging parameters were used: FOV = 240 x 240 mm2, echo time
(TE) = 1.97 ms, acquisition matrix = 128 x 128 and slice thickness = 8 mm. Total
acquisition time for B1+ profiles in all eight channels was 53 s. ΔB0 was measured
using the phase information from two gradient echo (GRE) images with different TE
values (TE1 / TE2 = 7.14 / 5.1 ms) and was incorporated into RF pulse design to
compensate for the phase accrual due to main magnetic field inhomogeneity (Figure
1.4b).
30
Figure 1.4 Additional inputs used in pulse design for the phantom experiments. a: Desired
excitation profile. b: Measured off-resonance map. c: Calibrated power correlation matrix of
the phantom-coil setup. d: Variable density spiral-in excitation k-space trajectory used in
experiments.
The subject-specific power correlation matrix Φ used for SAR prediction and
optimization was estimated using the automated Power Prediction and Monitoring
(PPM) technique described by Zhu and coworkers. (61). To accurately characterize the
field interference effects on SAR this technique estimates  by measuring in situ
individual channel forward and reflected power that correspond to the application of a
set of calibration RF pulses. By the law of conservation of energy, pfwd - prfl, gives
the net RF power delivered, which allows the assembling and solving of a set of Eq.
[1.2]-type linear equations but with the b’s as the coefficients and the entries of Φ as
the unknowns. The calibrated Φ matrix (Figure 1.4c) was used in parallel RF pulse
31
design via a regularization term (Eq. [1.9]) in order to trade off global SAR against
excitation fidelity.
The linear class LTA method (40) was used to design parallel RF pulses with a
90° target flip angle. The target excitation flip angle distribution θdes (Figure 1.4a) was
a homogenous 4 x 2 cm2 rectangular 2D profile blurred by convolving it with a
Gaussian kernel of full-width half-maximum (FWHM) = 1.2 cm to reduce ringing
artifacts in the resulting magnetization distribution. A variable density (80) inward
spiral trajectory (Figure 1.4d) was used to cover excitation k-space with the following
parameters: α = 2 (defines the amount of oversampling near the origin of the k-space),
sampling interval = 10 µs and duration = 7 ms (corresponding to 3-fold acceleration
with respect to a 21 ms non-accelerated RF pulse using constant rate spirals), in-plane
resolution = 3.78 mm, maximum gradient slew rate = 150 mT / m / s, and maximum
gradient amplitude = 40 mT / m.
Two different regularization terms, conventional and proposed, were used to
design parallel RF pulses. As in the simulations, in order to provide a fair comparison
of the global SAR effects of different regularization schemes, both NRMSE and
nominal flip angle were aligned between different parallel pulse designs. For fully
parallel transmission, this was achieved using different heuristically chosen
regularization parameters, β, and NRMSE was computed only inside the region where
the desired rectangular magnetization profile (Figure 1.4a) has flip angle values
greater than 0°, since accuracy of the B1 mapping algorithm diminishes for low flip
32
angles. Flip angle profiles of the designed RF pulses were measured using the
technique described earlier for B1+ map acquisition (specifically, designed parallel RF
pulses were played as saturation pulses followed by a multishot segmented turbo
FLASH acquisition with 4 segments). Imaging parameters were: FOV = 240 x 240
mm2 TE = 1.97 ms, acquisition matrix = 128 x 128, acquisition time = 40 s. Linearity
of the designed RF pulses and the parallel transmission system was assessed by
measuring the average flip angle over a range of transmit voltages. Actual global SAR
was experimentally measured using forward and reflected power readings during the
RF excitation period. In addition, expected power deposition into the phantom was
predicted by Eq. [1.2] and compared with the actual net power measurements.
1.4 Results
1.4.1 Water Phantom Simulations
For each of the experimental setups RF shimming with coefficients calculated
using the two different regularization terms were performed. Comparison of global
SAR was conducted at aligned NRMSE level of 0.99 for all experimental setups
(Figure 1.1a-c). For experimental setup A at the same NRMSE of 0.99 for example,
global SAR for RF shim weights were 0.15 W / kg with conventional and 0.1 W / kg
with proposed regularization terms. Including the global SAR knowledge into RF
shim weight design via proposed Φ-based regularization resulted in 34.9%, 9.7% and
27.5% decrease compared to conventional I-based regularization in average net power
deposition into the water phantom for experimental setups A, B and C, respectively.
33
Bloch simulation results of parallel RF transmission pulses designed for
experimental setup C are shown at Figure 1.2c,d for conventional and proposed
regularization terms, respectively. The two RF design approaches achieved
comparable fidelity producing the desired flip angle distributions with the desired flip
angle profile (Figure 1.2b).
Figure 1.5a shows the percentage global SAR benefit (at fixed NRMSE) of
using the proposed SAR-minimizing method versus the conventional method for
different acceleration factors (R = 1 and 2) and RF pulse design methods. Both linear
class LTA and STA pulse designs that accounted for electric field interactions resulted
in lower global SAR than those that ignored electric field interactions. Calculated
power correlation matrices of three different simulations are shown in Figure 1.5c.
The greatest SAR benefits were observed for setup B. For setup C, global SAR
differences between RF design schemes were minor due to a highly-diagonal power
correlation matrix that resembles a scaled identity matrix. Table 1.1 shows that
incorporating the Φ in STA RF pulse calculations results in lower global SAR for
every coil arrangement without sacrificing excitation fidelity. Global SAR decrease
was more significant for the arrays in setup A and B, for which stronger electric field
interactions resulted in large variations among the diagonal and off-diagonal elements
of the Φ. Although the use of the Φ instead of I in pulse design increased the sum of
all channel RF current amplitude squared for most of the experiments, as indicated by
34
the values in the third row of Table 1.1, it did not result in higher global SAR. This
result indicates that electric field interferences play an important role in global SAR.
35
Figure 1.5 Global SAR when the power correlation matrix is incorporated into parallel RF
pulse design. Values are reported as the percent improvement in global SAR with respect to
using a conventional regularization term for the same flip angle and excitation fidelity. Results
of different RF pulse design methods and acceleration factors for three different transmit array
setups are shown for the water phantom (a) and the human model (b). Calculated power
correlation matrices for three different array setups are shown for the water phantom (c) and
the human model (d).
36
Table 1.1 Comparison of STA parallel RF pulse behavior in a simulation involving imaging of a water phantom with various transmit
array configurations and acceleration factors.
Setup A
Setup B
R =1
R =2
I
SAR (W/kg)
0.097
0.109
NRMSE
0.021
Total RF (A2)
1584
Φ
R =1
I
R =2
R =1
R =2
Φ
I
Φ
I
Φ
I
Φ
I
0.619 0.661
0.100
0.123
0.667
0.723
0.115
0.116
0.854
0.866
0.021
0.020 0.020
0.020
0.020
0.020
0.020
0.022
0.022
0.021
0.021
1313
5028
2421
1533
8033
5429
1066
1048
3959
3954
37
Φ
Setup C
% SAR decrease
10.7
4319
6.4
18.2
7.8
1.4
1.3
The conventional RF pulse design approach is denoted by I (indicating that the power correlation matrix was replaced by the identity
matrix in the regularization term), and the proposed approach is denoted by Φ.
SAR = specific absorption rate in watts per kilogram. NRMSE = normalized root mean square error between desired and achieved
magnetization profile. Total RF = Integrated RF current amplitude (in amperes) square over all channels.
1.4.2 Human Mesh Simulations
In simulations using the human mesh model, larger global SAR benefits were
observed compared to water phantom simulations in all transmit array configurations
(Figure 1.5b). Both LCLTA and STA pulse design resulted in lower global SAR when
electric field interactions were incorporated. As was the case for water phantom
simulations, the greatest global SAR benefits were observed for setup B in which Φ
deviates significantly from a scaled identity matrix (Figure 1.5d). For setup C, the
global SAR benefit was more accentuated in the human body model than in the water
phantom, which can be explained in part by an increased variation amongst the
diagonal elements of Φ for the inhomogeneous human mesh compared with the
homogeneous water phantom.
1.4.3 Experiments
Prior to applying calculated RF pulses on the scanner, Bloch simulation results
of RF pulses with different regularization terms were used to align the NRMSE of the
magnetization distributions. Figure 1.6a,b represent the Bloch-simulated results of flip
angle profiles calculated with conventional and proposed regularization terms,
respectively. Both approaches resulted in NRMSE of 0.0319. The amplitude of the
designed RF pulse waveform in one of the channels is shown in Figure 1.7a. Notice
that incorporating Φ into RF pulse design resulted in local changes in the RF pulse
waveform to improve the SAR management of the pulse as a whole while preserving
the excitation fidelity.
38
Figure 1.6 Experimental results. a, b: Bloch equation simulation results for NRMSE-aligned
RF pulses calculated with conventional (a) and proposed (b) regularization terms. c: Shimmed
reference image used for transmit sensitivity mapping. d, e: MR images obtained using
parallel RF pulses designed with conventional (d) and proposed (e) approaches as saturation
pulses. f,g,h,i: Flip angle (f,g) and phase (h,i) maps of the conventional RF design with
transmit voltage 135V (f,h) and the proposed RF design with transmit voltage 130V (g,i).
39
To verify the flip angle profile in actual experiment, the calculated RF pulses
were used as a saturation pulse. An RF shimmed reference image was obtained from
selective excitation of all channels without magnetization preparation (Figure 1.6c).
Table 2 shows that the mean flip angle and NRMSE for the conventional and proposed
regularization terms were aligned over a range of transmit voltages (110 V - 150 V).
For the given input transmit voltage range, the LCLTA parallel transmit RF pulse
design resulted in a linear response of the system (Figure 1.7b). This validated the
linear class assumption used in the pulse calculation and also confirmed the linearity
of the system within the given input voltage range. Saturation effects resulting from
the designed 90° RF pulses can be seen in Figure 1.6d,e for 135V and 130V transmit
voltages of RF designs with conventional and proposed regularization terms,
respectively. Rectangular black regions within the phantom correspond to positions
where 90° flip angle was produced by the saturation pulse (i.e., the designed 90°
excitation pulse). Figure 1.6f,g show the flip angle maps of the designed RF pulses
which were extracted from the ratio between reference and saturation images. It is
clear from the figure that there is a good agreement between Bloch simulations and
experimental results. For the measured flip angle maps, calculated mean flip
angle / NRMSE ratios were 88.67 / 0.116 and 88.14 / 0.116 for RF pulses designed
with conventional (transmit voltage 135 V) and proposed (transmit voltage 130 V)
regularization terms, respectively.
40
Figure 1.7 RF pulse waveforms and RF net power a: Amplitude of the designed RF pulse
waveforms in one of the transmit channels. b: Linearity of the system and RF pulse design
process with respect to transmit voltage. c,d: Measured and predicted net power (in kW) of the
transmit array with a 7 ms LCLTA RF pulse. c: Conventional RF design method with transmit
voltage 135V. d: Proposed RF design method with transmit voltage 130V.
The forward and the reflected power of the designed RF pulses were measured
using the power meter. The average net power measurements from the RF power
amplifiers and predicted average net power deposition calculated according to Eq.
[1.2] with Φ and calculated pulse waveforms are shown in Table 1.2 for various
transmit voltages. Measured / predicted average net power for RF designs were 212.16
/ 237.81 W with conventional and 197.01 / 212.07 W with proposed regularization
41
terms. Including global SAR model into RF pulse design via regularization resulted in
~7.4% decrease in average net power dissipation for comparable average flip angle
and NRMSE. Figure 1.7c,d shows the net power measurements and predictions of
designed RF pulses. The net power measurements tend to be somewhat lower than the
predicted power values. This was attributed, in part, to the timing offset between
power measurement and the scanner's RF pulse update (every 10μs) and the temporal
averaging involved in power measurement.
42
Table 1.2 Experimental parallel RF pulse behavior
Proposed Parallel RF Pulse Design
Conventional Parallel RF Pulse Design
43
Transmit Voltage (V)
110
115
120
125
130
135
140
120
125
130
135
140
145
150
Mean Flip Angle
75.1
78.3
81.7
84.9
88.1
91.4
94.4
79.3
82.4
85.5
88.7
91.8
94.8
97.8
NRMSE
0.18
0.15
0.13
0.12
0.12
0.13
0.14
0.15
0.13
0.12
0.12
0.13
0.15
0.17
Measured Power (W)
142
155
168
182
197
213
228
168
183
197
212
228
246
261
Estimated Power (W)
152
166
181
196
212
229
246
188
204
221
238
256
274
294
Comparison of conventional and proposed parallel RF pulse design methods in terms of mean flip angle inside the region where the
desired magnetization profile has greater than 0° flip angle, normalized root mean square error NRMSE between desired and actual
magnetization distributions, measured power and predicted power.
1.5 Discussion
In this work, we have demonstrated the reduction in RF power deposition by
incorporating measured electric field interactions into pulse design for parallel
excitation. This work represents an original effort to incorporate a truly
subject-specific SAR prediction model into parallel RF transmission pulse designs and
to
further
validate
the
designs
in
MR
experiments.
The
use
of
an
experimentally-calibrated global SAR prediction model as an explicit regularization
term gives the user the flexibility to tradeoff SAR and excitation fidelity. By contrast,
strict constraint-based optimization approaches (29,36) (realized, for example, via
Lagrange multipliers) guarantee that the specified constraints, e.g. on excitation
fidelity (29) or on SAR (36), are always met. Within the parameter space allowed by
the constraints, the solution that minimizes the remaining optimization goals is then
selected. A strict-constraint-based approach is in fact possible using our experimental
global-SAR calibration method, and this could be valuable in ensuring that patientspecific global SAR is always maintained below a target value. Our current
regularization-based approach, however, is applicable to a broad range of pulse design
and optimization problems. It is fully applicable to the design of LTA parallel RF
pulses when the linear class assumption for the k-space trajectory holds. Linear class
assumption restrictions on LTA parallel RF pulse design can be overcome by using
regularization terms in design procedures which accept arbitrary excitation k-space
44
trajectories, such as the additive angle method (42) and the optimal control approach
(41).
It is possible to integrate explicit global SAR management into many of the
existing parallel excitation pulse design methods. The power correlation matrix-based
SAR tracking metric is simple in form (quadratic) and behave nicely (convex
functions), making integration straightforward. In the present work for example, the
SAR-tracking quadratic term introduced simply replaces a regularization term existing
already in the design method, resulting in minimum additional numerical burden. We
expect the impact of introducing the term on complexity to be small even in the more
involved optimal control design case (41), as the new composite metric to be
minimized remains convex (sum of quadratic functions).
Global SAR benefits of incorporating electric field interactions into RF pulse
design were validated in phantom and human body model simulations and in phantom
experiments. As was reflected in high NRMSE's for RF shimming simulations,
magnetization profiles for our RF shimming simulations were substantially different
from the desired magnetization profile. This deficiency could be reduced to some
extent by increasing the number of transmit elements or by using a target profile
phase-relaxed RF shimming algorithm. However, calculation of phase-relaxed RF
shimming coefficients (32) may stall in local optimal solutions, which would
complicate a fair comparison of the effects of different regularization schemes.
45
A power calibration system (61) was used to obtain subject-specific
information about electric field interactions and to predict RF power deposition for
arbitrary parallel RF transmission pulses. While results showed notable agreement
between power deposition predictions and experimental measurements, a significant
limitation of our current experimental setup can be identified. Given that the RF power
sensor in the present system is located at the output of the power amplifiers, the
system overestimates SAR in the imaged subject. At this location, the sensor’s power
readings include a significant cable loss component - a separate measurement
indicated that RF loss in the coaxial cables connecting the power amplifiers to the
coils accounts for over 50% of total RF power delivered by the RF power amplifiers.
This significantly impacts the structure of the calibrated power correlation matrix Φ,
making the entries on the diagonal dominate (and making Φ resemble a scaled identity
matrix). This setup can be improved and more significant SAR reduction can be
observed (81) by moving the power sensing location close to the transmit coils. The
improvement however, can be a challenge to implement as it requires a significant
portion of the power measurement instrumentation to be compatible with the 7 T
magnetic field.
1.6 Acknowledgements for Chapter 1
I would like to thank Dr. Hans-Peter Fautz from Siemens Medical Solutions in
Erlangen, Germany for collaboration on the flip angle mapping sequence. Dr. Graham
Wiggins is acknowledged for discussions on development of the coil array and
46
interface used for parallel transmission. I would also thank to Dr. Riccardo Lattanzi
for helpful discussions on simulations.
47
CHAPTER 2: Maximum Efficiency RF Shimming: Theory and Initial
Application for Hip Imaging at 7 Tesla
Deniz CM, Alon L, Brown R, Sodickson DK, and Zhu Y
Maximum Efficiency RF Shimming: Theory and Initial Application for Hip Imaging at
7T
Manuscript in progress
Author contributions:
Cem Murat Deniz: Manuscript draft, study design, RF shimming software, data
acquisition, data analysis, data interpretation, literature research
Ryan Brown: MR coils and interface, data acquisition, manuscript editing
Riccardo Lattanzi: Study concept, SNR analysis software, manuscript editing
Leeor Alon: Power calibration system and software, manuscript editing
Daniel K. Sodickson: Study concept, manuscript editing
Yudong Zhu: Study concept, data interpretation, manuscript editing
48
Peer reviewed abstracts from the chapter:
Deniz CM, Brown R, Lattanzi R, Alon L, Sodickson DK, and Zhu Y
Maximum Efficiency RF Shimming
In Proceedings of the 20th Scientific Meeting, International Society for Magnetic
Resonance in Medicine, Melbourne, Australia, page 3479, 2012.
Deniz CM, Brown R, Alon L, Sodickson DK, Zhu Y, and Lattanzi R
MRI of the Hip at 7T Using RF Shimming with 4-Channel Excitation
In Proceedings of the ISMRM Workshop on Ultra-High Field Systems &
Applications: 7T & Beyond: Progress, Pitfalls & Potential, Lake Louise, Alberta,
Canada, 2011.
49
2.1 Abstract
Radiofrequency shimming with multiple channel excitation has been proposed
to increase the transverse magnetic field uniformity and reduce specific absorption rate
at high magnetic field strengths (≥ 7 Tesla) where high-frequency effects can make
traditional single channel volume coils unsuitable for transmission. In the case of deep
anatomic regions and power-demanding pulse sequences, optimization of transmit
efficiency may be a more critical requirement than homogeneity per se. This work
introduces a novel method to maximize transmit efficiency using multiple channel
excitation and radiofrequency shimming. Shimming weights are calculated in order to
obtain the lowest possible net radiofrequency power deposition into the subject for a
given transverse magnetic field strength. The method was demonstrated in imaging
studies of articular cartilage of the hip joint at 7 Tesla. We show that the new
radiofrequency shimming method can enable reduction in power deposition while
maintaining an average flip angle or adiabatic condition in the hip cartilage. Building
upon the improved shimming, we further show the signal-to-noise ratio in hip cartilage
at 7 Tesla can be substantially greater than that at 3 Tesla, illustrating the potential
benefits of high field hip imaging.
2.2 Introduction
The promise of improved morphological and functional imaging due to higher
signal-to-noise ratio has motivated the pursuit of ultra-high field MRI (≥ 7 T).
However, ultra-high field MRI is challenging, due to inhomogeneities of the
50
transverse radiofrequency magnetic field (B1+), which compromise image quality, and
specific absorption rate constraints, which limits the strength of MR excitation at
depth.
RF shimming (19,23) and parallel excitation (28,29) techniques using multiple
transmit channels have been shown to allow significant reductions in B1+ field
inhomogeneities. While RF shimming has limited capability to provide homogeneous
B1+ over large regions, local phase-only RF shimming (24) which aims for B1+ phase
coherence / constructive interference in small target regions, such as the prostate, have
been shown to provide reasonable homogeneity and increase in B1+ field for a given
transmit RF power. Depending on the particular application in question, different RF
shimming methods have been proposed which, for example target B1+ magnitude and
phase homogeneity (19), target B1+ magnitude homogeneity without regard for B1+
phase (82), tradeoff B1+ homogeneity for SAR minimization (72,83,84), pursue B1+
homogeneity by sequential application of two different RF shim weights (85), or
facilitate the adiabatic condition of the RF pulse (86,87).
In this paper a maximum efficiency RF shimming approach is presented,
which, given any coil-subject setup, calculates a set of RF shim weights that
maximizes B1+ strength for any given level of RF power deposition into the subject.
Field interference is the fundamental principle underpinning multi-port or array coil
transmission. While desirable B1+ interference patterns are sought after for managing
the excitation profile (as is the case in shimming for B1+ homogeneity or in
51
full-fledged parallel RF transmission), concomitant electric field interference impacts
RF power deposition. The present approach, which not only accounts for transmit
sensitivity patterns but also for subject-specific electric field interference effects on
global SAR and net RF power, has a unique advantage over existing methods that aim
at increasing power efficiency by performing guided manipulation of the B1+ field
only.
The feasibility of the new RF shimming method was demonstrated in imaging
studies of hip articular cartilage, an application that is clinically significant yet
technically challenging. Accurate assessment of hip anatomy and function has become
a critical concern in recent years, after it was shown that the success of surgical
procedures aimed at delaying or preventing hip osteoarthritis by correcting the bony
abnormalities associated with femoroacetabular impingement (88) depends on the
absence of irreversible degenerative changes in the hip cartilage (89). However the
evaluation of the hip cartilage is currently a challenge even at 3 T and normally
requires administration of exogenous contrast agent to capture areas of abnormalities
with sufficient contrast and SNR (90).
Maximum efficiency RF shimming can be an enabling technical solution to
advance high field hip imaging and benefit clinical practice. Hip imaging represents an
application that targets a deep anatomical region and demands good SNR.
Conventional RF shimming at ultra high field tends to face difficulties managing RF
52
power. Furthermore, as the thickness of the hip articular cartilage, which covers the
femoral head and the acetabulum, ranges approximately from 1.5 to 5 mm (91)
decreased power deposition could be leveraged to increase spatial resolution and/or
SNR by allowing increases in the achievable flip angle and / or the number of
refocusing pulses.
Following a description of the maximum efficiency RF shimming method,
experimental calibration of the inputs for the proposed RF shimming method is
explained. Using experimental power and B1+ map measurements, maximum
efficiency RF shimming was compared with non-targeted unit RF shimming using
different RF pulse types (sinc and adiabatic). In addition, simulations incorporating
subject-specific calibration data, including individual channel B1+ maps and transmit
power correlation matrix, were used to compare the proposed method with three
existing RF shimming methods. Finally, in order to illustrate the gains at high field
strength in anatomical regions of significant clinical interest, quantitative SNR
comparisons in hip articular cartilage between 3 T and 7 T were conducted.
2.3 Materials and Methods
2.3.1 Maximum Efficiency RF Shimming
RF shimming (19,23) was proposed to correct B1+ inhomogeneities by
optimizing the relative amplitudes and phases of multiple transmit elements driven
53
with a common RF waveform. Flexibility to control the relative amplitude and phase
of the individual transmit elements can also be exploited to increase transmit
efficiency. This section describes the maximum efficiency RF shimming method
which aims to maximize B1+ strength for any given level of RF power deposition into
the subject.
In order to obtain the complex-valued RF shim weights that correspond to the
amplitude and phase modulation associated with maximum transmit efficiency, we use
a transmit efficiency metric defined as B1+ magnitude squared per unit dissipated
power, following earlier work by Zhu et al. (92). Using the superposition principle of
linear systems, the net B1+ and electric field at each spatial location r and at each time
t can be defined as:
N
N
n 1
n 1
B1 (r)   w( n)b( n) (r) and E(r)   w( n )e( n ) (r)
[2.1]
where N is the number of transmit elements, and the weights w(n) specify the amplitude
and phase modulation of the driving RF current waveform in the nth channel of a
transmit array. The complex-valued b ( n ) (r ) and e( n ) (r ) represent, respectively, the
B1+ and electric fields corresponding to unit weighting on the nth channel and zero
weights on the others. Choosing an ROI, the values of B1+ at all M spatial locations
included in the ROI can be combined in matrix form as B1  Cw where C is an M x N
matrix with C mn  b ( n ) (rm ) . The average B1+ squared in the ROI can be expressed as:
average B1
54
2
 w H Γw
[2.2]
where the B1+ correlation matrix Γ  M 1C H C , and H denotes the conjugate transpose.
Here, Γ is an N x N positive-definite complex Hermitian matrix.
The total RF power deposited by the parallel transmit array into the object at
time t can be calculated by taking the following volume integral over the object and
substituting the linear superposition of the electric fields from Eq. [2.1] :
P
 (r)
2
v
2
E(r ) 2 dv  w H Φw
[2.3]
where σ is the electrical conductivity, and Φ defines the N x N positive-definite
Hermitian power correlation matrix whose (i, j)-th element is given by:
i, j 
1
 (r )e(i ) (r )*  e( j ) (r )dv
2 v
[2.4]
and * indicates complex conjugate.
A rapid calibration scheme to measure experimentally the elements of the
power correlation matrix in Eq. [2.4] has recently been described (60,61,66). Once Φ
is known, RF power dissipation (Eq. [2.3]) (66) can be determined for any possible set
of RF shimming weights w, allowing prediction of the global SAR consequences of
any imaging sequence (84). For cases in which radiative losses and coil losses are
significant, the resulting predicted power dissipation is an upper bound on overall RF
power deposition in the subject; for the more common situation in which body losses
are the dominant contribution, the predicted power dissipation more closely tracks
global SAR in body tissues. Ref. (66) addresses these considerations in detail, as well
as identifying potential improvements to the calibration process. The entries of the
55
matrix C can be measured with any B1+ mapping technique, allowing the evaluation of

Γ. Using the derived expressions for the average B1 squared and the total RF power
deposition for any RF shim weights w, the transmit efficiency metric can be defined as
(92):
w H Γw
 H
w Φw
[2.5]
By streamlining the power calibration and B1+ mapping, the efficiency metric,
η, can be practically evaluated in vivo. In practice, it is convenient to use units of μT
squared per Watt. In the conventional single channel case, Γ and Φ reduce to scalars,
and the metric captures B1+ squared per unit power, compatible with existing practice.
In the multi-channel transmission case, different w's correspond to different efficiency
in general. In addition, given the bilinear form in both numerator and denominator, η
is independent of any overall scale factor in the RF shimming weights (and therefore
independent of any overall changes in transmit voltage).
Depending on the RF shimming coefficients, a given transmit array loaded
with a given subject operates over a range of efficiencies. Searching for the RF shim
weights that maximize η can be accomplished using various numerical optimization
algorithms. However, it can be shown that calculating the maximum and minimum of
η can be treated as a generalized eigenvalue problem which does not require a
nonlinear search and guarantees the calculation of the global optimum. From the
solution obtained with numerical calculations (for example with the Matlab function
56
eig(Γ,Φ)), the largest eigenvalue and its corresponding eigenvector represent the
maximum transmit efficiency and the maximum efficiency RF shim weights, w,
respectively. Calculated maximum efficiency RF shim weights can be used in
experiments to obtain the highest possible transmit efficiency for the given coil-patient
configuration.
Figure 2.1 Experimental setup. a: Cross-sectional schematic of the coil and phantom setup. b:
Photograph of a loop/stripline module. The conductor layout of the active element of the
stripline and loop can be seen. c: Photograph of the 7 T experimental setup with a molded
human phantom. Loop/stripline coil modules indicated by numbers 1-5 were used in hip
experiments and the remaining modules were removed.
2.3.2 System Hardware and RF Coil Array
We evaluated the benefits of maximum efficiency RF shimming at 7 T,
targeting hip imaging as an exemplary application. Experiments were performed on a
57
whole body 7 T scanner (Magnetom, Siemens Medical Solutions, Erlangen, Germany)
equipped with an eight-channel parallel transmit system (1kW peak power per
transmit channel) and a gradient system capable of achieving peak gradient strength of
40 mT / m and a slew rate of 150 T / m / s. A 10-channel transmit / receive modular
array (93) (Figure 2.1a and c) consisting of five loop / stripline modules was used for
RF excitation and reception. Loop coils were 8 x 20 cm2 with a solid copper shield 2
cm above the loop conductors to reduce radiation loss and coupling to neighboring
coils and undesired anatomy such as the arms. The loops were tuned to 297.2 MHz
using 16 distributed capacitors of approximately 16 pF. Striplines with 15 cm length
and 2 x 3 x 15 cm3 Teflon dielectric were tuned using two capacitors of approximately
4.3 pF at opposing ends of the stripline. The striplines were centered with respect to
the loop coils (Figure 2.1b) such that their arrangement provided a naturally decoupled
loop/stripline module similar to that described in Ref. (94). Both loops and striplines
were capacitively matched to 50 Ω while loaded with a body-size agar phantom with
uniform electrical properties of average human muscle at 297.2 MHz (εr ≈ 58, σ ≈ 0.77
S / m.). The array of loop/stripline modules was placed around the phantom or human
torso with two posterior, one anterior and two lateral modules. The four loops closest
to the targeted ROI (inside modules 1-4 in Figure 2.1c) were used for RF transmission
and reception, while the remaining 6 elements (loop inside module 5 and striplines
inside modules 1-5) were used for RF reception only.
58
In order to evaluate the maximum efficiency RF shimming approach in terms
of RF power reduction per B1+ squared, forward and reflected power readings were
obtained from four channels via an RF switch (Dual 16 x 1 MUX, National
Instruments, Austin, TX, USA) with a power sensor (NRP-Z11, Rhode & Schwarz,
Munich, Germany) connected to directional couplers (C8705, Werlatone, New York)
located at the penetration panel.
A 3T MRI scanner (Verio, Siemens Medical Solutions, Erlangen, Germany)
equipped with a gradient system capable of achieving peak gradient strength of 40
mT / m and a slew rate of 150 T / m / s was used to image the hip of the same
volunteers, and the SNR in the hip region was compared with that achieved using
maximum efficiency RF shimming at 7 T. The body coil was used for RF excitation
and a 32-element cardiac coil array (Invivo, Orlando, FL) was placed around the
pelvis for signal reception at 3 T.
2.3.3 RF Shimming Experiments
The use of local transmit coils called for RF power limits to restrict possible
tissue heating caused by the induced electric fields. To predict the spatial positions
with the greatest electric fields, a finite difference time domain (FDTD) (Computer
Simulation Technology, CST, Darmstadt, Germany), simulation (2 mm3 spatial
resolution) was performed in which a loop coil representative of that used in the
experiments was positioned adjacent to a uniform elliptical cylindrical phantom whose
size and electrical properties were similar to the human torso and muscle, respectively
59
(major diameter = 47.2 cm, minor diameter = 24.7 cm, electrical conductivity = 0.77
S/m, and dielectric constant = 58). To experimentally determine the safe operating
limit of a single coil, the temperature of a 3.6 kg lamb slab was recorded using
fluoroptic temperature probes (Luxtron M3300, Lumasense Technologies, Santa
Clara, CA, USA) during RF irradiation. The fluoroptic probes were inserted
approximately 5 mm into the lamb at four locations, including those with maximal
electric fields according to the FDTD simulation; 1) coil drivepoint, 2) capacitor
opposite the drivepoint, 3) capacitor midway along the side conductor, and 4) center of
coil. Distance from the coil conductor to the lamb was approximately 2 cm. RF power
was delivered to the coil for 10 min while the time-averaged (10 s) power was
monitored by vendor-provided hardware. Following RF irradiation, temperature
monitoring was continued for 2 mins to assess heat diffusion from locations adjacent
to the temperature probes. No temperature increase was observed during the post-RF
period. Assuming a linear relationship between RF irradiation and the rate of
temperature change, the safe operating limit was defined as the 10 s time-averaged
power input necessary to produce a 1°C temperature increase during a 10 min RF
irradiation period. For a single coil, the total power limit was hence determined to be
10W. In the parallel transmit experiments, power limits were applied using
conservative criteria that assumed the worst-case scenario in which electric-fields due
to individual transmit elements add constructively. Since four transmit loops were
used in the present study, this approach limited the individual input power to 16 times
60
less than the limit for a single loop (0.625W). In addition, 10 s and 6 min average RF
power was monitored for each channel in real time.
Calculation of the maximum efficiency RF weights requires B1+ profiles for
each transmitter along with the power correlation matrix. B1+ mapping was performed
following the method described in Ref. (79) by performing two separate
measurements using selective excitation of all channels without magnetization
preparation and with a saturation pulse on one channel at a time to produce spatialdependent B1+ map of the channel. B1+ magnitude maps, Figure 2.2c, in an axial plane
were obtained with sinc saturation pulses followed by a spoiled turbo fast low-angle
shot (FLASH) imaging acquisition with selective excitation from all channels.
Additional turbo FLASH imaging, using one coil for excitation at a time, were used to
calculate relative B1+ phase distribution for different coils (Figure 2.2d). Relevant
imaging parameters used for B1+ mapping were: field of view (FOV) = 360 x 360
mm2, echo time (TE) = 1.97 ms, acquisition matrix = 128 x 128, TR = 3 s, saturation
thickness = 10 mm, and slice thickness = 8 mm. Total acquisition time for B1+ maps in
all four channels was 27 s. An ROI over the hip articular cartilage was defined on one
of the images (Figure 2.2b) and the corresponding Γ-matrix (Figure 2.2e) was
calculated using the individual coil B1+ profiles.
The subject-specific power correlation matrix Φ (Figure 2.2f) was estimated
from measurements of the individual channel forward and reflected power, using the
power sensors connected to the directional couplers, associated with a set of
61
calibration RF pulses (60,61,66). The net power measurements (forward minus
reflected) during each predefined calibration pulse allows a set of linear equations
resembling Eq. [2.3] to be assembled and solved, using the predefined values of w as
known coefficients and assigning entries of Φ as unknowns. The calibrated Φ-matrix,
the Γ-matrix and the ROI were used to calculate the maximum efficiency RF shim
weights for the hip articular cartilage, following the procedure described earlier in the
text.
62
Figure 2.2 Steps required for the calculation of the maximum efficiency RF shimming
weights. a: Axial GRE image of one volunteer with the approximate stripline/loop coil
module locations overlaid in red (transmit/receive loops and receive-only striplines) and green
(receive-only loops and striplines). b: Zoomed GRE image with the target hip cartilage ROI
(red) for maximum efficiency optimization. c: B1+ amplitude maps for each transmit loop. d:
B1+ phase maps for each transmit loop. e: Γ-matrix calculated using the B1+ maps in the ROI.
f: Calibrated power correlation matrix, Φ, measured using the forward and reflected power
measurements of the system.
63
Because experimental evaluation of several shim methods in the same
volunteer would require excessive examination time, we used experimentally acquired
B1+ maps and the calibrated Φ-matrix as simulation inputs for the offline comparison
of four RF shimming strategies: the proposed maximum efficiency RF shimming,
non-targeted unit RF shimming, local phase matching RF shimming, and
uniformity-targeted RF shimming. The non-targeted unit RF shimming delivers RF
with unit amplitude and zero phase offset to all transmit channels. Local phase
matching (24) aims to increase the constructive B1+ interference in the target ROI by
adjusting
the
transmit
phase
offset
between
each
transmit
channel.
Uniformity-targeted RF shimming (19) aims to increase B1+ homogeneity inside the
ROI by adjusting the relative transmit amplitude and phase to each channel through a
least squares solution.
In addition to the comparison of different RF shimming strategies in
simulations, net average power deposition and flip angle maps were measured to
compare the transmit efficiency achieved with the maximum efficiency RF shimming
to that achieved with non-targeted unit RF shimming. The flip angle distribution
resulting from both RF shimming methods, with acquisition matrix 256 x 256, was
measured using the method detailed above with saturation pulses played
simultaneously on all transmit channels. High resolution axial spoiled GRE images of
the hip region were acquired with maximum efficiency and non-targeted unit RF
shimming using the following parameters: acquisition matrix = 512 x 512, spatial
64
resolution 0.7 x 0.7 x 2 mm3, TE/TR = 4.73/400 ms, FOV = 360 x 360 mm2,
bandwidth (BW) = 300 Hz / pixel, and acquisition time 210 s. Additionally, net
average power deposition was measured using power sensors during GRE image
acquisition.
Four volunteers (three men and one woman; age = 37.5 ± 9.2 years) were
imaged in an axial plane through the left hip articular cartilage. Volunteer imaging
was performed with protocols approved by the New York University School of
Medicine Institutional Review Board, and written informed consent was obtained from
volunteers.
Maximum efficiency RF shimming does not inherently increase B1+
homogeneity within the selected ROI. However as shown before, adequate B1+
homogeneity can be achieved in a small ROI, such as the prostate (24). On the other
hand, special classes of RF pulses, such as the adiabatic pulse, inherently improve flip
angle uniformity. A drawback of adiabatic pulses is the high RF power deposition
required to satisfy the adiabatic condition at every voxel within the ROI. Since
maximum efficiency RF shimming aims to maximize B1+ field while minimizing the
power deposition, adiabatic pulses could benefit from the proposed RF shimming
method. We tested this hypothesis both in simulation and in experiments for an
adiabatic half passage (AHP) RF pulse (95). Experimentally measured individual
channel B1+ profiles (Figure 2.2c and d) and an AHP RF pulse of length 10.24 ms
were used in spinor-domain Bloch simulations (78) to calculate the flip angle
65
distribution. For the maximum efficiency shim and the non-targeted unit shim, the
adiabatic condition at the position in the ROI with the weakest B1+ was determined by
calculating the frequency response of the AHP RF pulse over a range of transmit
voltages using Bloch simulations; the adiabatic condition at this position was satisfied
when the z-component of magnetization at zero frequency was approximately zero and
not affected by further transmit voltage increase. Net power deposition of AHP RF
pulses with maximum efficiency shim and non-targeted unit shim was measured with
the transmit voltage for each shim set such that the AHP RF pulse satisfied the
adiabatic condition at all locations within the ROI. Flip angle distributions of the AHP
RF pulses with maximum efficiency shim and non-targeted unit shim were measured
using the technique described earlier for B1+ map acquisition (specifically, AHP RF
pulses were played as saturation pulses followed by a turbo FLASH acquisition). In
order to examine the off-resonance effect on AHP RF pulse, off-resonance maps were
calculated from individual receive coils using the three point "Dixon method" that
decomposes fat, water, and off-resonance through a least-squares calculation with
complex gradient echo images at TE = 4.08, 4.42, and 4.76 ms (96). A combined
off-resonance map was formed by weighting the contribution of each coil by the
square of its signal intensity. The combined off resonance map was smoothed using a
median filter with 5 x 5 kernel size.
66
2.3.4 SNR Comparison
The SNR in the hip articular cartilage achieved with maximum efficiency RF
shimming at 7 T was compared with that achieved at 3 T. High resolution spoiled
axial GRE images of the hip region were acquired with low flip angles at both 3 T and
7 T, using the parameters given in the previous subsection. Due to different sample T1
in each magnet, low flip angle excitation was utilized to avoid magnetization
saturation effects that would complicate SNR analysis. Noise data were acquired with
zero transmit voltage and used to compute the noise covariance matrix of the receive
coils. The GRE images and the noise covariance matrix were used to generate SNR
maps following a method by Kellman and McVeigh (97).
Flip angle maps of the GRE acquisitions, with acquisition matrix 256 x 256,
were obtained using the flip angle mapping protocol explained in the previous section.
As the flip angle mapping algorithm is more prone to error at low flip angles, the flip
angle maps were acquired with higher transmit voltages than those used in the GRE
acquisitions. The acquired flip angle map was then scaled by the ratio of GRE transmit
voltage to flip angle mapping transmit voltage. The scaled flip angle maps were
interpolated to a matrix size of 512 x 512 to match the matrix size of the GRE
acquisition. For fair comparison between 3 T and 7 T, we removed the effect of spatial
flip angle variations by normalizing the SNR maps with the sine of the flip angle at
each voxel. Three of the four volunteers were imaged at both 3 T and 7 T for SNR
comparison.
67
Figure 2.3 Representative axial GRE images of one volunteer at 7 T (volunteer 1), acquired
with non-targeted unit RF shimming (a) and maximum efficiency RF shimming (b). Zoomed
images of the hip articular cartilage show that low signal caused by destructive RF
interference with non-targeted unit RF shimming (arrow in c) is restored using maximum
efficiency RF shimming (d).
2.4 Results
Representative 7 T axial GRE images with non-targeted unit RF shimming and
maximum efficiency RF shimming for volunteer 1 are shown in Figure 2.3a and
Figure 2.3b, respectively. Non-targeted unit RF shimming resulted in B1+
inhomogeneity and large signal intensity variations in the hip region and a local signal
68
drop indicated by the arrow in Figure 2.3c. The maximum efficiency RF shimming,
with a targeted ROI covering the left hip articular cartilage (Figure 2.3b), resulted in
improved homogeneity in the hip region (Figure 2.3d) and ~2.4 times increase in
transmit efficiency, as calculated with Eq. [2.5]. In achieving similar average flip
angles over the ROI in the cases of unit RF shimming (flip angle 27.6° ± 12.4°) and
maximum efficiency RF shimming (flip angle 25.3° ± 12.1°), respectively, the net
average energy deposition were measured to be 155 W and 58.8 W.
Transmit efficiency comparisons between different RF shimming methods are
summarized in Table 2.1. For all volunteers, maximum efficiency RF shimming
provided the highest transmit efficiency. Among the RF shimming methods, local
phase matching provided the second highest transmit efficiency (on average 22%
lower than that of the maximum efficiency method). In all volunteers, uniformity RF
shimming resulted in lowest transmit efficiency. This could be attributed to the
method's priority of increasing B1+ uniformity over increasing average B1+. The RF
power deposition benefit using maximum efficiency RF shimming compared to
non-targeted unit RF shimming for all volunteers is shown on the last row of Table
2.1. Table 2.2 shows that in imaging experiments the net RF power deposition with
maximum efficiency shim weights was on average 39% lower than that required to
achieve similar flip angles with the non-targeted unit RF shim. The experimentally
quantified RF power deposition benefit of using maximum efficiency RF shimming
was in good agreement with the RF power deposition benefit quantified with
69
simulations (last rows of Table 2.1 and Table 2.2). Calculated maximum efficiency
RF shim weights varied substantially among the volunteers due to differences in body
composition and size (Table 2.3).
Figure 2.4 Adiabatic half passage RF pulse results : B1+ maps with (top row) and without
(bottom row) maximum efficiency RF shimming. AHP pulses provided improved B1+
uniformity (columns two and three) over standard sinc pulses (column one) in the hip articular
cartilage. h is the measured off resonance map.
70
Table 2.1 Comparison of four RF shimming methods in simulations based on experimentally acquired transmit sensitivity and power
correlation data: A: Non-targeted Unit RF shimming, B: Maximum Efficiency RF Shimming, C: Local phase matching RF shimming
from Ref. (24), and D: Uniformity RF Shimming from Ref. (19). The RF power deposition benefit of using maximum efficiency RF
shimming versus non-targeted unit RF shimming was calculated by comparing estimated power depositions per average unit squared
flip angles.
Volunteer 1
Shim
Method
A
B
C
Volunteer 2
D
45.9° 40.0° 44.1° 17.8°
71
Flip Angle
±
±
±
Power (W)
Efficiency
(η)
B
C
27.0° 23.4° 30.7°
D
9.0°
A
B
C
28.0° 23.9° 30.8°
B
Benefit
D
41.8° 34.5° 46.5° 13.2°
±
4.1°
7.6°
5.2°
6.4°
2.6°
19.4° 15.1° 20.5°
231.3 73.9 218.5 50.5
148.8 76.3 151.5
1.8
147.7 80.2 147.7 44.1
283.5 138.2 274.7 134.5
9.97 23.34 9.46
5.27
1.78
7.83
6.62
9.96
9.23
±
±
±
±
±
4.8°
12.0°
9.4°
13.9°
3.3°
1.83
9.22
RF Power
Deposition
C
±
6.51
±
7.6°
A
±
7.51
±
D
±
6.58
±
Volunteer 4
±
14.3° 11.2° 11.2°
Estimated
A
Volunteer 3
58%
32%
26%
29%
8.57
2.08
Table 2.2 Experimentally measured net power deposition and corresponding flip angle with non-targeted unit RF shimming and
maximum efficiency RF shimming. Experiments using non-targeted unit RF shimming are denoted by A, and experiments using
maximum efficiency RF shim weights are denoted by B. The RF power deposition benefit of using maximum efficiency RF shimming
versus non-targeted unit RF shimming was calculated by comparing average net power depositions per average unit squared flip
angles.
Volunteer 1*
Shim Method
Flip angle
Volunteer 2
Volunteer 3
Volunteer 4
B
A
B
A
B
A
B
27.6° ± 12.4°
25.3° ± 12.1°
6.3° ± 2.3°
5.8° ± 2.2°
4.3° ± 2.6°
3.8° ± 2.8°
6.9° ± 3.2°
5.9° ± 2.6°
155.33
58.85
5.28
2.74
6.80
3.69
18.10
8.76
72
A
Net Power
Deposition (W)
RF Power
Deposition
55%
39%
30%
Benefit
*: GRE images and power measurements were obtained with higher flip angles compared to other volunteers
33%
Table 2.3 Calculated maximum efficiency RF shimming weights and measured individual anatomical dimensions for all volunteers.
Transmit Coil Number
1
‖ ‖
2
∡
Body Dimensions (cm)*
3
4
‖ ‖
∡
‖ ‖
∡
‖ ‖
∡
A to C
P to C
L to C
R
73
Volunteer 1
1
216.3°
0.44
31.3°
0.45
0.6°
0.22
0°
7.1
10.8
7.6
2.1
Volunteer 2
0.76
273.4°
0.71
17.7°
1
342.7°
0.36
0°
7.6
9.6
8.9
2.5
Volunteer 3
1
316.0°
0.5
45.2°
0.77
345.6°
0.57
0°
8.9
12.1
12.6
2.0
Volunteer 4
1
1.59°
0.45
92.1°
0.67
348.1°
0.61
0°
7.7
12.1
12.3
2.2
* Anterior (A), posterior (P), left (L), center of femoral head (C), and radius of femoral head (R).
The power deposition and B1+ distribution of an AHP RF pulse with maximum
efficiency RF shim and non-targeted unit RF shim weights were assessed on volunteer
2. The maximum power required to meet the adiabatic condition at points inside the
ROI with the weakest B1+ distribution was 411 W for maximum efficiency shim and
789 W for non-targeted unit RF shim. Both shims resulted in a maximum of 2.31 μT
instantaneous B1+ field in the weakest B1+ location. Bloch simulations of AHP RF
pulses with the specified voltages resulted in a mean of 1% ± 3% z-magnetization,
which corresponded to remarkably uniform flip angle distribution of 89.4° ± 1.7°. Flip
angle distributions for maximum efficiency RF shim and non-targeted unit shim in the
ROI are shown for Bloch simulations (Figure 2.4c and Figure 2.4d) and experiments
(Figure 2.4d and Figure 2.4e). Whereas the Bloch simulation resulted in
approximately uniform 90° flip angle, experimental flip angle maps show increased
deviation in some locations which appear to correspond to locations with high main
magnetic field gradients (Figure 2.4h). This was confirmed in additional Bloch
simulations that incorporated the off-resonance maps. The AHP pulse provided a clear
improvement in B1+ uniformity over standard sinc excitation pulses (Figure 2.4a and
Figure 2.4b).
Figure 5 shows GRE images of volunteer 4 at 7 T and 3 T (Figure 2.5a and
Figure 2.5b) with flip angles (Figure 2.5c and Figure 2.5d) of 5.7° ± 2.6° and 9.7° ±
1.2° in the hip cartilage, respectively. Quantitative SNR maps of acquired GRE
images are shown in Figure 2.5e and Figure 2.5f. Figure 2.5e and Figure 2.5f clearly
74
show the actual SNR benefits of moving to higher field strength. Despite the lower flip
angles at 7 T (Figure 2.5c) compared to 3T (Figure 2.5d), the average SNR was
greater: 8.3 ± 4.9 at 7 T versus 6.9 ± 2.8 at 3 T (Figure 2.5e and Figure 2.5f). After
dividing the SNR maps by the sine of the flip angle at each voxel, the normalized SNR
was 43.4 ± 18.2 at 3 T and 83.5 ± 38.7 at 7 T. Averaged over all volunteers, 7 T
normalized SNR was 133% greater than that at 3 T (Table 2.4).
Table 2.4 SNR results in the hip articular cartilage of the volunteers at 3 T and 7 T.
Volunteer 2
3T
Flip Angle
SNR
7T
9.6° ± 0.9° 4.9° ± 1.9°
8.8 ± 3
10.7 ± 5.9
Volunteer 3
3T
7T
3T
7T
10.2° ± 1.4°
5.1° ± 1.9°
9.7° ± 1.2°
5.7° ± 2.6°
6.0 ± 2.2
7.7 ± 3.3
6.9 ± 2.8
8.3 ± 4.9
43.4 ± 18.2
83.5 ± 38.7
Normalized SNR 53.4±20.1 124.5±52.8 34.6 ± 13.8 96.9 ± 51.9
Normalized SNR
gain at 7T
Volunteer 4
2.3
2.8
75
1.9
Figure 2.5 SNR comparison at 3 T and 7 T Axial GRE images (top row) and zoomed flip
angle (middle row) and SNR maps (third row) from volunteer 4 at 7T (left column) and 3T
(right column).
76
2.5 Discussion
In this work, we have demonstrated a maximum efficiency RF shimming
method that finds the lowest possible net RF power deposition into the subject for a
given flip angle inside the ROI. The proposed RF shimming method calculates optimal
shim weights which increase transmit efficiency by utilizing in vivo calibrated
predictions of the net RF power deposition along with B1+ field maps. Previous RF
shimming methods (24,87) only utilize B1+ constructive interference without
accounting for electrical field effects or power deposition. In addition, the transmit
efficiency metric defined in Eq. [2.5] enabled the global optimum RF shimming
weights to be efficiently calculated, without the need for computationally intensive
nonlinear search algorithms (86,98).
The proposed RF shimming method was compared in simulations using
experimental B1+ maps and power correlation matrices with three different RF
shimming methods: a) non-targeted unit RF shimming; b) uniformity-targeted RF
shimming (19), which has been used to address the challenge of signal inhomogeneity
that has hindered ultra-high-field imaging; and c) local phase matching RF shimming
(24), which has been found to perform effectively in FDTD simulations (98). The
simulations showed maximum efficiency RF shimming increased the transmit
efficiency compared to other methods by including calibrated subject-specific RF
power deposition predictions in RF shimming calculations. Some of the simulations
were further corroborated by imaging experiments, which confirmed the validness of
77
the comparison (last rows of Tables 1 and 2). In addition to the global RF power
deposition behavior documented here, local SAR properties of the proposed method
should be analyzed and compared with other RF shimming methods. However, for
such a comparison, full knowledge of actual electric field information inside the
subject is required. In future work, FDTD simulations can be used for such
comparisons, since determining the actual electric field inside the subject is not yet
feasible.
Hip imaging at 7 T was chosen as a representative application to demonstrate
maximum efficiency RF shimming. In fact, imaging the hip joint is challenging due to
its deep anatomical location, which requires large transmit voltages and results in
severe B1+ inhomogeneities at high field strength. In our volunteer experiments, power
measurements for sinc and AHP RF pulses in axial GRE acquisitions confirmed up to
50% decreases in RF power deposition while maintaining average flip angle
distributions. This suggests that SAR-intensive pulse sequences, such as turbo spin
echo (commonly used at lower magnetic field strengths for clinical hip imaging due to
high SNR and contrast-to-noise ratio), may become feasible at 7T using multiple-coil
transmission with maximum efficiency RF shimming. Our results show that the flip
angle-normalized SNR in the hip articular cartilage was on average 2.3 times greater
at 7 T than at 3 T. Furthermore, we showed that optimizing RF power deposition in a
ROI tends to reduce B1+ inhomogeneities within it. One limitation of our SNR
comparison study is the difference in receive coil sensitivities at 7 T and 3 T due to
78
variation in coil size and structure. However, the hip lies at a similar depth (5 to 12 cm
from the body surface) as the heart, suggesting that the cardiac array used at 3 T may
serve as a reasonable SNR benchmark.
In this study, GRE pulse sequences were used for the SNR comparison because
they are less SAR-intensive and therefore facilitated a comparison between 3 T and
7 T with our existing transmit hardware setup and safety limits. While GRE images
are not widely used for clinical morphological assessment of the hip articular cartilage,
they are employed for biochemical assessment in which T1 and T2* are measured
(99,100). In these applications, which could be facilitated at 7 T using maximum
efficiency RF shimming, improved SNR would result in more reliable T1 or T2*
quantification, or could be traded off for increased spatial resolution, which is
essential to resolve the thin layer of articular cartilage in the hip joint (91).
In summary, the maximum efficiency RF shimming method utilizes both
electric and magnetic field measurements corresponding to the in situ transmit array
and is subject to promptly calculate transmit shim weights that minimize the power
required for a given flip angle. An accompanying benefit of the proposed shim method
was that it provided reasonable flip angle uniformity in a clinically relevant ROI. The
shim method was successfully demonstrated in experimental 7 T MRI of the hip
articular cartilage, confirming the present method’s potential to outperform other shim
methods in terms of efficiency.
79
2.6 Acknowledgements for Chapter 2
I would like to thank Dr. Hans-Peter Fautz from Siemens Medical Solutions in
Erlangen, Germany for collaboration on the flip angle mapping sequence. Dr. Graham
Wiggins is acknowledged for discussions on SNR comparison. I would like to thank
Dr. Bei Zhang for her help in FDTD simulations, Kellyanne Mcgorty for her help on
sequence protocols and Dr. Assaf Tal for useful discussions on adiabatic RF pulses.
80
CHAPTER 3: Subject-specific Proactive Management of Parallel RF
Transmission
Author contributions:
Cem Murat Deniz: Chapter writing, study design, RF Pulse design, Matlab software,
data acquisition and analysis
Leeor Alon: Power calibration system and software, chapter editing
Ryan Brown: MR coils and interface
Daniel K. Sodickson: Study concept, chapter editing
Yudong Zhu: Study concept and design, data interpretation, chapter editing
81
3.1 Abstract
MR scanners have predefined power delivery and reflection handling
capabilities. Any practical RF pulse used on a scanner must be designed with those
capabilities in mind. In parallel transmission, the interactions between individual
channels, and between these channels and the imaged subject, play an important role
in power delivery in determining the demands placed upon the power amplifiers. By
using pre-scan based individual channel forward and reflected power calibration, we
designed parallel RF excitation pulses obeying the forward / reflected peak and
average power limits of the RF power amplifier. Additionally, global SAR limits were
incorporated in the RF pulse design. Results showed that the prediction capability of
this new calibration method enables the design of parallel RF excitation pulses
respecting strict and multifaceted power limits.
3.2 Introduction
When applying parallel RF transmission in practice, coupling and interaction
taking place in the multi-port coil structure as well as in the subject can significantly
affect individual channel RF power transmission towards and away from the subject,
posing challenges to transmit channel instrumentation and safety monitoring. Tracking
and predicting these effects and proactively managing power transmission is important
for ensuring a smooth scan. In this chapter, PPM technique (60,61,66) described in
Section 1.3.6 for global SAR is further extended to individual channel forward and
reflected power for any RF excitation. The forward and reflected power predictions
82
were used proactively to design constrained parallel RF excitation pulses to meet the
RF power requirements. The constrained parallel RF excitation pulses designed in this
way were played out on the MR scanner, and resulting forward and reflected power
measurements as well as excitation fidelity were compared with unconstrained pulse
designs or designs constrained by global SAR only.
3.3 Materials and Methods
3.3.1 Individual Channel Power Prediction
Our PPM technique (60,61,66) uses in situ individual channel forward and
reflected power measurements that correspond to the application of a set of calibration
RF pulses to estimate the global power correlation matrix Φ. This scheme can be
extended to model and predict individual channel forward or reflected power by using
the notation of Section 1.3.2 and the following equations:
l
Pfwd
( pt )  b Hpt Φlfwd b pt and Prfll ( pt )  bHpt Φlrfl b pt
[3.1]
l
( pt ) and Prfll ( pt ) are the lth channel's measured forward and reflected
where Pfwd
power at time instant pΔt, respectively. b pt  b1, pt  bL , pt 
T
defines the
predefined input calibration weights from L transmit channels similar to Eq. [1.2],
denotes the transpose and
H
T
denotes the complex conjugate transpose. By using the
predefined calibration weights and measuring the associated power, forward, Φ lfwd ,
and reflected, Φlrfl , power correlation matrices of all channels can be estimated.
83
There are various possibilities for leveraging channel-by-channel power
prediction capability: 1) Given the peak power rating of the power amplifiers assigned
to drive the parallel transmission channels, knowing in advance the peak power
requirements for the individual channels allows the user to proactively adapt the
excitation pulse design and / or reconfigure the transmit hardware (e.g., by updating
the power combination scheme applied to the component amplifier units). 2) Given the
reflected power handling capacity of the amplifiers / circulators on the parallel
transmission channels, knowing in advance large peak reflected power for the
individual channels similarly allows the user to implement software- and / or
hardware-based mitigation strategies. 3) Checking the individual channel power
predictions against actual measurements, or comparing the matrices determined at
baseline and those updated periodically afterwards, provides diagnostics that can
detect in real-time system changes caused by, for example, hardware failure, system
instability or patient position change. These diagnostics can be used as triggers to
suspend scanning as needed. In other words, using the power prediction models both
in planning and in monitoring may avert amplifier peak power or voltage standing
wave ratio faults, protection hardware breakdown, and excessive SAR due to system
failure.
Potential use of individual channel power prediction models in detecting /
diagnosing system changes in real-time (option #3 above) was explored in detail in
Ref. (66). In this chapter, the first two options described above will be explored by
84
using constrained parallel RF transmission pulse design. Forward and reflected power
correlation matrices will be used to guide parallel RF transmission pulse design with
strict peak and average forward and reflected power constraints.
3.3.2 Constrained RF Pulse Design
The calibration of forward and reflected power correlation matrices enables the
prediction of an individual channel's forward and reflected power given an arbitrary
RF pulse at any time instant. This property enables proactive power transmission /
resource management through RF pulse calculation. One way of integrating power
prediction capability into RF pulse design is to use the following convex inequalities:
l
b Hpt Φlfwd b pt  Pfwd
, peak , l  1, , L
[3.2]
b Hpt Φlrfl b pt  Prfll , peak , l  1, , L
[3.3]
l
  b Hpt Φlfwd b pt  Pfwd
, ave , l  1,  , L
[3.4]
  b Hpt Φlrfl b pt  Prfll ,ave , l  1,, L
[3.5]
p
p
l
l
where Pfwd
, peak represents the lth channel's peak power delivery capacity, Prfl , peak
l
represents the lth channel's tolerance to reflected peak power, Pfwd
, ave represents the lth
channel's average power delivery capacity, Prfll ,ave represents the lth channel's average
power reflection capacity and α = 1 / RF pulse width. In addition to the constraints
involving individual power predictions, predefined maximum global SAR limits
allowed by FDA guidelines (20) can be incorporated using the global power
85
correlation matrix of Eq. [1.10]. Using STA approximation and variables defined in
Section 1.3.3, RF pulses for parallel excitation can be calculated by solving the
following optimization problem:
bˆ full  arg min Afullbfull  mdes
bfull
2
2
such that b H Φ b  globalSARLimit
full full full
l
b Hpt Φlfwd b pt  Pfwd
, peak
l , p
b Hpt Φlrfl b pt  Prfll , peak
l , p
[3.6]
l
  b Hpt Φlfwd b pt  Pfwd
l
, ave
p
  b Hpt Φlrfl b pt  Prfll ,ave
l
p
T
where b full  b1Tt , b T2 t  b TPt  is the concatenation of the coil RF pulse waveforms
for each time point pΔt, and Φfull is the matrix containing global power correlation
information to be used in conjunction with b full as explained in Eq. [1.10].
This optimization problem can be solved by using a range of efficient
strategies for convex optimization since the power correlation matrices are positive
definite and the constraints are quadratic convex functions. Convex optimization
guarantees that a global optimum, if it exists, will be found within a defined error
bound. The complexity of the optimization problem increases with the RF pulse
length, the number of channels, and the desired magnetization resolution. The
complexity of a similar optimization problem (36) was reduced using least-squares
projections (101) in order to find a small number of basis vectors which still contains a
good approximation to the original problem but reduces the optimization search space
86
drastically. We followed steps described in Ref. (36) to reduce the complexity of the
optimization problem, specifically using Lanczos algorithm with Gram-Schmidt reorthogonalization steps (102). New formulation of the convex optimization problem
using reduced-basis vectors still includes the exact power constraints as defined in Eq.
[3.6] and can be solved efficiently by using a variety of well established solvers. In
this work, the SeDuMi (103) v1.2.1 solver, interfaced with YALMIP (104), was used
to solve the reduced basis convex optimization problem.
3.3.3 Experimental RF Pulse Design
Experiments were performed on a Siemens whole body 7 T Magnetom scanner
(Erlangen, Germany) equipped with an eight-channel parallel transmit system (1kW
peak power per transmit channel) in order to demonstrate the subject-specific
proactive management of parallel transmission RF pulse design by using the calibrated
power correlation matrices. The eight channel coil array (Figure 1.3a), phantom
(Figure 1.3b) and power measurement setup described in Section 1.3.6 were used in
this study as well. B1+ calibration was performed on an axial slice at the isocenter
following the method and the parameters described in Ref. (79) and Section 1.3.6,
respectively.
Global Φ and channel-by-channel forward Φ lfwd and reflected Φlrfl power
correlation matrices were calibrated by measuring in situ individual channel forward
and reflected power for a set of calibration RF pulses. Power sensors were connected
to directional couplers at the output of each RF amplifier, The calibrated power
87
correlation matrices were used in constrained parallel transmission RF pulse design in
order to limit the global SAR (by using Φ, Figure 3.1a), peak and average forward
power (by using, Φ lfwd , Figure 3.1b), and peak and average reflected power (by using
Φlrfl , Figure 3.1c).
Figure 3.1 Example of calibrated power correlation matrices. a: global power correlation
matrix, b: forward power correlation matrix of transmit channel 4, and c: reflected power
correlation matrix of transmit channel 4.
Figure 3.2 Desired excitation profile and k-space trajectory a: Desired 2D axial excitation
profile, and b: spiral-in excitation k-space trajectory
88
Unconstrained, global SAR constrained, and fully constrained (global SAR,
peak forward and reflected power, average forward and reflected power) RF pulses
were designed using the target excitation profile shown in Figure 3.2a, using custom
code and a custom-built GUI (see Appendix) developed in Matlab (version 7.13,
MathWorks, Inc., Natick, MA, USA). A constant rate spiral-in excitation k-space
trajectory (Figure 3.2b) was used with duration = 4.5 ms (corresponding to 4.3-fold
acceleration with respect to unaccelerated k-space), excitation resolution = 3.8 mm,
sampling interval = 10μs, maximum gradient slew rate =150 mT / m / s and maximum
gradient amplitude = 40 mT / m. In the present feasibility study, the following power
l
limits were used in constrained RF pulse design: global SAR = 3.2 W / kg, Pfwd
, peak =
l
l
700 W, Prfll , peak = 50 W, Pfwd
, ave = 50 W, Prfl ,ave = 25 W. Forward and reflected power
in eight channels were measured with a sampling rate of 5μs while calculated RF
pulses were used in a 3D GRE acquisition with the following parameters: FOV = 240
x 240 mm2, TR = 80 ms, TE = 5 ms, matrix size = 64 x 64, number of slices = 48, and
slice thickness = 5mm. Measured powers were compared to channel-by-channel
forward and reflected power predictions based on calibrated power correlation
matrices.
3.4 Results and Discussion
Axial GRE images and Bloch simulation results for the excitation profiles of
RF pulses designed with different constraints are shown in Figure 3.3. The NRMSEs
of the desired and obtained magnetization from Bloch simulations were 0.0220 /
89
0.0224 / 0.0258 for unconstrained / global SAR constrained / fully constrained RF
pulse designs. All designs resulted in similar acceptable excitation fidelity. The
increase in NRMSE in constrained RF pulse design shows that in order to meet the
strict constraint requirements, some compromise in excitation fidelity was required.
However, this 0.3% increase in excitation error is hardly noticeable on the GRE
images (Figure 3.3d, f).
Figure 3.3 Bloch simulation results and axial GRE images of designed RF pulses are shown in
a and d for unconstrained design, b and e for global SAR constrained design, c and f for fully
constrained design. Red circle in f represents the phantom boundary.
Figure 3.4 shows the individual channel forward power predictions and actual
power measurements for Channel 4. There is notable agreement between power
predictions and experimental power measurements (similar agreement was observed
90
for net power measurements and predictions as illustrated in Figure 1.7).
Approximately 10% lower measured peak power was observed compared to
predictions. This could be explained by mismatch between the RF and the power
meter raster times, and by temporal averaging involved in power measurement. In
order to further emphasize the necessity of power correlation matrix calibration for
proactive management of parallel RF transmission, the reflected power in Channel 4
was estimated by neglecting the contributions of other channels to the reflected power
in that channel, i.e. by using single-element reflected power correlation matrix shown
in Figure 3.4e. This resulted in significant deviations from measured reflected power,
as indicated by red arrows in Figure 3.4a, and inaccurate maximum power estimation.
Figure 3.4 Comparison of individual channel actual power measurements (a) and power
prediction (b) using calibrated reflected power correlation matrix (d) for Channel 4. Assuming
91
the reflected power correlation matrix as shown in e (i.e. neglecting reflected power
contributions from other coils) resulted in reflected power predictions (c) which deviate
significantly from measured power, as indicated by red arrows in a.
92
Table 3.1 Power comparison of RF pulses with different power constraints. Italic channel
numbers indicate which transmit channel had the peak power displayed in the table for the
particular measurement. Measured global SAR, forward and reflected peak and average power
values for the fully constrained RF pulse design can be compared with the estimated values
using the last two columns.
Measured
Estimated
Global SAR
Fully
Fully
Constrained
Constrained
Constrained
5.14
2.93
2.3
2.4
FWD Peak
1103.2
916.2
683.9
700
(W)
(ch3)
(ch1)
(ch4)
RFL Peak
86.5
67.5
46.4
(W)
(ch3)
(ch3)
(ch3)
FWD Average
65.3
40.3
30.7
(W)
(ch1)
(ch1)
(ch1)
RFL Average
3.7
2.2
1.59
(W)
(ch2)
(ch3)
(ch3)
Unconstrained
Global SAR
(W/kg)
50
33.5
1.96
Table 3.1 summarizes the benefits of RF pulse design with the guidance of
calibrated power correlation matrices. RF pulse design without any constraints
violated some of the limits in various channels (column Unconstrained). Designing RF
pulses with only a global SAR constraint successfully enforced the global SAR limit,
but violated peak and reflected power limits in some channels (column Global SAR
Constrained). All violations were removed by designing the RF pulse with all
93
constraints active (column Fully Constrained). Proper guidance can also be verified by
the last column of the Table 3.1, in which the power prediction matches well with
experimental measurements in the indicated channels. In Figure 3.5, the measured
forward power of Channel 5 and reflected power of Channel 3 show that violations of
peak power limits (indicated by red lines) are removed by guiding constrained RF
pulse design with calibrated power correlation matrices.
Figure 3.5 Measured power for RF pulses designed with different power constraints. Red
horizontal lines indicate the power limits used in constrained RF pulse design. Left column:
forward power measurements in a representative channel, Channel 5. Right column: reflected
power measurements in a representative channel, Channel 3.
In this work, we demonstrated the subject-specific proactive management of
parallel transmission using calibrated power correlation matrices and RF pulse design
with convex optimization Strict power limits on patient safety and on MR scanner
hardware are guaranteed during RF pulse design.
94
CHAPTER 4: RF Energy Deposition and RF Power Requirements in Parallel
Transmission with Increasing Distance from the Coil to the Sample
Deniz CM, Lattanzi R, Zhu Y, Wiggins G, and Sodickson DK
RF Energy Deposition and RF Power Requirements in Parallel Transmission with
Increasing Distance from the Coil to the Sample
In Proceedings of the 17th Scientific Meeting, International Society for Magnetic
Resonance in Medicine, Honolulu, page 4802, 2009.
Author contributions:
Cem Murat Deniz: Abstract draft, study design, simulations, data analysis
Riccardo Lattanzi: Simulation software, abstract editing, data interpretation
Graham Wiggins: Study concept and design
Yudong Zhu: Study concept
Daniel K. Sodickson: Study concept and design, data interpretation, abstract editing
95
4.1 Abstract
Minimizing SAR while maintaining a homogenous excitation is one of the
principal challenges associated with the use of ultra high magnetic field strengths. We
investigated the SAR behavior and the power requirements for parallel transmission as
the gap between transmit elements and the surface of the object is increased. Various
simulated geometrical arrangements of coil elements around a sphere and a cylinder
were explored: one in which an increasing number of coils of fixed size were placed
around the object, and another in which a fixed number of coils with increasing radius
were arranged at increasing distance from the object. We found that global SAR and
peak SAR during parallel excitation decreases with lift-off for spherical object-coil
setup, approaching the lowest SAR allowed by electrodynamics (i.e. the ultimate
intrinsic SAR) while the input power requirements to achieve the desired excitation
increases rapidly with lift-off. On the other hand, optimal coil lift-off that minimizes
the global SAR and input power requirements were found for the cylindrical objectcoil setup. Thus, for parallel transmission there are SAR benefits in moving coils away
from the object, but RF power requirements may represent a practical limiting factor.
4.2 Introduction
Parallel transmission with multiple RF coils (28,29) enables homogeneous
excitations at ultra high magnetic field strengths, while minimizing the specific
absorption rate over the entire volume of the sample (29,72). However, electric fields
generated by transmit coils placed close to the body may cause dangerous hotspots,
96
even though average global SAR remains small over the duration of excitation. On the
other hand, if the coils are placed at a distance from the body, the RF power required
to achieve a given flip angle distribution may be high, and it may be feared that this
will result in increased global SAR. Furthermore, increasing the distance between the
transmit array and the sample widens the area of overlap between individual coil
sensitivities, which may compromise the performance of parallel transmission
techniques. SAR dependence on array geometry in parallel transmission was studied
by Katscher et al. (49), by changing the relative orientation between two transmit coils
placed at a fixed distance from the center of a spherical object. For a two-coil
experimental setup, Katscher et al. (49) found that the angular tolerance of the coil
positions was typically ~20° - 30° with a tolerance of 10% increase in SAR compared
to the optimal coil SAR deposition.
In this work we investigated global, peak and local SAR behavior and the
corresponding RF power requirements with respect to the separation between the
transmit elements and the surface of the object, in the case of a dielectric sphere and
cylinder at 3 T and 7 T main magnetic field strengths. Ultimate intrinsic global SAR
(72), which is defined as the lowest possible global SAR consistent with
electrodynamics for a particular excitation profile but independent of transmit coil
design, was used to compare how closely different transmit array designs were able to
approach the best possible configuration. Surface-contoured rectangular coils and
97
circular coils of different sizes and numbers were used to identify the optimal lift-off
distance between the transmit array and the object surface.
4.3 Materials and Methods
A dyadic Green’s function (DGF) formulation (105) was used to derive the
full-wave electromagnetic fields inside a dielectric sphere / cylinder from a complete
basis of current modes, which were defined on a spherical / cylindrical surface
concentric with the object. The calculated complete basis set of current modes was
employed to calculate ultimate intrinsic global SAR (72). In order to calculate the
appropriate weighting of the current modes, uniform target excitation profiles were
chosen in the transverse plane for spherical, and coronal and transverse planes for
cylindrical simulation setups. Minimum global SAR for finite arrays of transmit loop
coils were calculated using current mode weights for parallel transmission aimed at
simultaneous global SAR minimization and B1+ homogeneity (106). The
corresponding input RF power requirements for calculated coil weights were
estimated by adding the RF power dissipated in coil conductors to the RF power
deposited in the sphere. In addition to sample and coil losses accounted for in the
spherical geometry, cylindrical simulations incorporated losses due to eddy currents
into the input RF power requirements by modeling the conductive magnetic shield
around the cylinder.
98
Figure 4.1 Transmit array geometries for spherical simulations. a: Belt-like design in which
coil size is kept constant and the number of coils is increased during lift-off. b: Symmetric
design in which the number of coils is kept constant and coil radius is increased during lift-off.
Increasing the distance between the object surface and the center of transmit
elements requires an increase in either number or size of the transmit coil elements. In
this work, both lift-off strategies were simulated for spherical and cylindrical
simulation setups. Figure 4.1 illustrates an example of transmit array geometries for
spherical simulations using both lift-off strategies. For the increased coil number
strategy, an increasing number of loop coils were arranged like a belt around the
sphere equator, fixing coil radius to 5 cm ("belt-like design," Figure 4.1a). For the
increased coil size strategy, a fixed number of coils were symmetrically packed around
the sphere, with individual coil radii scaling up with increasing lift-off ("symmetric
99
design," Figure 4.1b). In both simulation strategies, a 15 cm radius dielectric sphere
was used with the following average brain tissue properties (107): dielectric constant
εr = 63.1 / 52, conductivity σ (S/m) = 0.46 / 0.55 for 3 T / 7 T.
Figure 4.2 Transmit array geometries for cylindrical simulations. a: Array design in which
coil size is kept constant and the number of coils is increased during lift-off. b: Array design
in which the number of coils is kept constant and coil size is increased during lift-off.
Figure 4.2 illustrates transmit array geometries used for cylindrical simulations
using two different lift-off strategies: 1) increasing the number of coils (Figure 4.2a)
and 2) increasing the coil size (Figure 4.2b). A cylindrical object of radius 15cm and
length 40 cm was used in both simulations. Since the cylindrical simulation setup
100
resembles application typical body more than a typical head, dielectric properties of
dog skeletal muscle were used.
The excitation of a uniform target profile on a transverse plane through the
center of the sphere was simulated for the case of a 32 x 32 EPI excitation trajectory,
using a SAR minimization algorithm for parallel transmission (29,72). Similarly,
transverse and coronal planes through the center of the cylinder were simulated using
24 x 24 and 18 x 24 EPI excitation trajectory, respectively. The complete current basis
set was defined on the spherical and cylindrical surfaces where the individual coils are
located in order to calculate the ultimate intrinsic global SAR. Calculations were
performed in MATLAB (Mathworks, Natick, USA) for different lift-offs, coil
numbers and field strengths (3 T and 7 T). Convergence tests of the ultimate global
SAR optimization, by changing the maximum order of the basis function expansion,
resulted in 13122 / 18281 current modes in the spherical / cylindrical simulation basis
sets for full convergence.
4.4 Results and Discussion
The target excitation profile was achieved in all cases. Figure 4.3 shows
minimum global SAR and RF power requirements as a function of the distance of the
finite arrays to the surface of the sphere. Results are presented for 3 T and 7 T main
field strengths and for different coil designs (belt-like and symmetric). Each plot is
normalized to the ultimate intrinsic SAR of the corresponding main magnetic field
strength, which notably remains constant for different lift-offs. In the ultimate case,
101
local SAR also does not change with lift-off, suggesting that there is a single optimal
electromagnetic field distribution that minimizes SAR while maintaining profile
fidelity, and it can be always achieved by choosing the appropriate combination of
modes in the basis set.
Figure 4.3 Optimized global SAR and RF power requirements versus lift-off , for the belt-like
(left column, a-c) and symmetric (right column, b-d) array design in spherical phantom. Each
plot is normalized to the ultimate intrinsic SAR at the corresponding magnetic field strength.
It is apparent from Figure 4.3a,b that global SAR is reduced, approaching
more closely the theoretical smallest value, ultimate intrinsic global SAR, as coils are
moved further from the object in both belt-like and symmetric designs at both 3 T and
102
7 T. However, when the same B1+ field distribution is used as a target, the
corresponding RF power requirements increase dramatically with increasing radius
(Figure 4.3c, d). Both global SAR and RF power requirements are higher at 7 T than at
3 T in all cases. RF power requirements for the 24-element symmetric array are lower
than for the 12-element array when the coils are close to the object, but power
requirements grow more rapidly with lift-off, since individual coil dimensions increase
and lead to larger dissipation.
Spatial distributions of local SAR in the center of excitation k-space and peak
SAR during the entire excitation are shown in Figure 4.4 for different lift-offs, in the
case of the belt-like array design for spherical object. It appears that when the coils are
near the surface of the sphere, electric fields generated by the coils are larger and may
cause higher RF energy deposition. Additionally, the increase in the number of coils
during lift-off can also be a contributing factor in the decreasing peak local SAR.
Figure 4.5 illustrates the optimal global SAR and RF power requirements for
the cylindrical object simulations using coronal and transverse target excitation FOV.
In all the simulations uniform target excitation profile was achieved while the
remaining degrees of freedom were used to decrease the global SAR of the calculated
RF pulses. As coils moved further from the object global SAR approached the
ultimate intrinsic global SAR (Figure 4.5a). Figure 4.5b indicates that the global SAR
minimization is more effective using larger numbers of coils: lower global SAR is
achieved in 32 coils as compared to 16 coils for the same lift-off distance. Both global
103
SAR and RF power requirements in both designs were higher at 7 T than at 3 T main
magnetic field strength. In contrast to the spherical simulations, an optimal coil lift-off
that minimizes RF power requirements was found for cylindrical object simulations.
In this work, we found that for parallel transmission there are SAR benefits in
moving the transmit coils away from the object, especially at higher field strengths.
Global SAR was found to decrease monotonically for the spherical case. On the other
hand, an optimum lift-off distance with minimum RF power requirements was
observed for particular coil geometries for the cylindrical case. Peak local SAR
decreases with lift-off in all cases. However, the increase in corresponding RF power
requirements may constitute a practical limitation to these benefits. There were a few
notable differences between the spherical and cylindrical simulations. The conductive
shield was not modeled for spherical simulations and losses due to eddy currents were
not included in the RF power requirements. Results for the cylindrical case could be
affected by the particular choice of placing the coils, i.e. rectangular coil size and
number were adjusted only in one dimension. Ultimate intrinsic global SAR is
independent of coil lift-off and can be used in this case as an absolute reference.
Ultimate intrinsic global SAR was approached with finite coils as lift-off distance and
number of transmit coils were increased.
In summary, we showed that there will be SAR benefits of moving RF coils
away from the subject when power requirements are well compensated. These
104
findings will serve as important guide for improving existing RF transmit coil designs
for practical parallel transmission.
Figure 4.4 Local SAR vs lift-off for the sphere . Peak SAR (top) and local SAR (bottom)
versus lift-off for the belt-like array design, at 3T and 7T. Normalized spatial SAR distribution
(base-10 log scale) within the FOV, during excitation of the center of k-space is shown for the
smallest (1 cm), and intermediate (10.9 cm) and the maximum (20.9 cm) lift-off value.
105
Figure 4.5 Optimized global SAR and RF power requirements versus lift-off for the cylinder.
Two different cylindrical phantom designs A (a) and B (b) are used as shown in Figure 4.2.
Results from both coronal (left column) and transverse (right column) FOVs are illustrated.
An optimal coil lift-off that minimizes the RF power requirements was observed. Each plot is
normalized to the ultimate intrinsic SAR at the corresponding magnetic field strength.
106
CHAPTER 5: Sparse Parallel Transmit Excitation Trajectory Design for Rapid
Inner-Volume Excitation
Deniz CM, Chen D, Alon L, Brown R, Fautz H-P, Sodickson DK, and Zhu Y
Sparse Parallel Transmit Excitation Trajectory Design for Rapid Inner-Volume
Excitation
In Proceedings of the 19th Scientific Meeting, International Society for Magnetic
Resonance in Medicine, Montreal, Canada. page 4434, 2011.
Author contributions:
Cem Murat Deniz: Abstract draft, study design, RF pulse design, data acquisition, data
analysis, literature survey
Dong Chen: subspace OMP method and software
Leeor Alon: Power measurement software
Ryan Brown: MR coils and interface
Hans-Peter Fautz: Flip angle mapping sequence
Daniel K. Sodickson: Study concept, abstract editing
Yudong Zhu: Study concept, abstract editing
107
5.1 Abstract
Tailored inner-volume excitation on whole-body scanners is often limited by
long 3D RF pulses. Effective pulse length reduction with parallel transmission
requires careful selection of the excitation k-space trajectory. In this work,
twomethods of determining sparse excitation trajectories were compared for parallel
transmit pulse design in the small-tip angle and large-tip-angle regimes: a) a subspace
Orthogonal Matching Pursuit algorithm, and b) a single-step thresholding algorithm.
Reasonable inner-volume excitations with a pulse length of less than 9 ms were
achieved using an eight-channel transmitter on a whole-body human 7T scanner.
5.2 Introduction
Tailored inner-volume excitation presents many challenges on whole-body
MRI systems, such as maximum gradient strength and slew rate limitations, the
selection of robust excitation k-space trajectories, and transmit field inhomogeneity for
high-field systems. Selection of the excitation k-space locations is one of the most
crucial decisions in RF pulse design as it directly impacts image quality and scan time.
This section briefly describes the excitation k-space concept and clarifies the
requirements of selecting a trajectory for a given MRI application.
5.2.1 Excitation k-space
The excitation k-space formalism is closely related to the concept of k-space
used more familiarly in MR imaging (6,7). In order to traverse (imaging) k-space, the
gradient magnetic fields, generated by x, y and z gradient coils, are superimposed
108
upon the main magnetic field. During MR measurements, imaging k-space is filled
with MR signal S(t) while driving the gradient coils simultaneously. Using the MR
signal equation neglecting decay terms, this process at any time instant t can be
described by:
S (t )   q(r)eik (t ) r dr
[5.1]
R
where q(r) is a factor which is mainly proportional to local magnetization density ρ(r)
at location r and R is the imaging volume. Imaging k-space locations, k(t), are defined
by
t
k (t )    G ( )d
[5.2]
0
where G(τ) represents the gradient waveforms and γ is the gyromagnetic ratio. As can
be seen from Eq. [5.1], encoded signal in imaging k-space is the Fourier representation
of the magnetization density distribution, while position r and spatial-frequency k are
Fourier transform pairs. This formalism helped the MRI community to better
understand and visualize the signal acquisition mechanism, which then formed a basis
for new acquisition approaches as parallel MRI (12,13).
A k-space approach can also be applied to the design of RF excitation pulses
(69). Using the STA approximation and neglecting the relaxation terms T1 and T2, the
transverse magnetization, Mxy, at time T can be described as a function of the applied
RF, B1(t), and gradient fields:
109
T
M xy (r )  i M 0  B1 (t )e
 i r 
T
t G ( ) d dt
[5.3]
0
where M0 is the initial magnetization before applying RF. Defining a spatial frequency
variable k(t) as
T
k (t )    G ( )d
[5.4]
t
the excitation k-space is generated by applied gradient fields during RF transmission.
Both imaging and excitation k-spaces defined by Eqs. [5.2] and [5.4] are
specified by applied gradient fields. In excitation k-space, the spatial frequency
variable k(t) is defined as the integral of the remaining gradient field compared to the
imaging k-space which is defined as the integral of the elapsed gradient field. This
difference is a natural result of the applied gradient field's effect on the transverse
magnetization phase distribution. As time passes, phase distribution of the transverse
magnetization that is excited by a STA RF pulse at time instant t evolves with the
gradient field applied until time T. On the other hand, in imaging k-space, until MR
signal is acquired, the phase distribution of the transverse magnetization after RF
excitation evolves while the gradient fields are applied for imaging. For that reason,
the imaging k-space is defined by the integral of the elapsed gradient field. The
excitation k-space formalism can be used to design STA RF excitation pulses (69) and
some special classes of LTA RF excitation pulses (76). One such special class of pulse
is the linear class, for which the k-space trajectory satisfies the following linear class
assumptions: 1) k(t) starts and ends at the center of excitation k-space, 2) k(t) can be
110
decomposed into a sequence of inherently refocused subtrajectories, in which STA
subpulses can be maintained. However, for LTA excitations which do not satisfy the
linear class assumption, the excitation k-space trajectories defined in Eq. [5.3] and
[5.4] may not be optimal, and our intuition must be adjusted.
Selection of the excitation k-space excursion and sampling density is one of the
major decisions for RF excitation pulse design. In the image domain, the chosen
excitation resolution specifies the smallest possible excitation volume and the
minimum transition width of the sharp edges required in RF pulse excitation. The
three dimensional excitation resolution in the image domain, Δr, is inversely
proportional to the three dimensional excitation k-space extent, kmax, with
 r  1 / 2k max , indicating that increased excitation resolution requires wider excitation
k-space coverage. Once a target excitation k-space extent has been chosen, the RF
excitation pulse design problem still requires definition of the density with which the
continuous excitation k-space will be discretely sampled. As is the case for MR
imaging k-space, the Nyquist-Shannon sampling theorem (108,109) defines the
excitation k-space sampling density requirements to enable excitation of the spins
without aliasing in the defined excitation field-of-view (xFOV). Aliasing of the
excitation / image occurs when a continuous RF / free induction decay (FID) signal is
digitized at a rate that is insufficient to capture the changes in the signal. This
sampling requirement in excitation k-space can be achieved by defining the xFOV and
obtaining the excitation k-space sampling interval, Δk, via k  1/ xFOV .
111
In MRI, imaging k-space data is acquired sequentially using phase and
frequency encoding generated by gradient fields. In every TR, lines in k-space are
filled with the acquired signal obtained after RF pulse excitation. This flexibility of
acquiring different k-space lines within different TRs enables the acquisition of high
resolution images. However, excitation k-space must be covered for every TR. This
requirement imposes a maximum possible RF length and excitation resolution
depending on the local properties of the body, e.g. T1 and T2*, which is the main
reason that most MRI applications use short (<< T2*) slice selective or nonselective RF
pulses.
The advent of parallel MRI (12,13) enabled faster MRI signal acquisitions by
reworking the imaging k-space sampling density requirements with spatially distinct
sensitivities from multiple receiver channels supplementing the spatial encoding that is
typically performed by gradients. In parallel imaging, undersampled imaging k-space
is acquired during MR signal acquisition and the full image is reconstructed using
receive sensitivity profiles after MR signal acquisition. Similarly, in parallel
transmission (28,29), the excitation k-space sampling density requirements can be
reduced by using multiple RF excitation coils and their sensitivities. Now, shorter RF
pulses can be achieved without aliasing in the volume of interest. The selection of
excitation k-space locations to be traversed during RF pulse excitation must be defined
while RF pulse length, excitation fidelity and gradient specifications are kept in mind.
The next section briefly surveys different excitation k-space location selections for
112
selective RF excitation pulse design both in one channel and in multiple channel
systems. From now on, the term k-space will be used to refer to excitation k-space.
5.2.2 Selection of Excitation k-space Locations
The dimension of the traversed k-space specifies the selectivity of the
excitation RF pulse in the image domain. For example, unidirectional slice selection
gradients with sinc RF pulses are widely used to excite spins in a specified slice. Since
slice selection gradients traverse a line in the k-space  0,0, kz  | kz  (kmax , kmax ) ,
their selectivity in the image domain is restricted to one dimension only. Assuming a
uniform transmit coil sensitivity over space, all spins within the selected transverse
slice will be excited. Figure 5.1 demonstrates the excitation k-space traversal of the
slice selection gradient and the location of the excited spins. The k-space extent, kmax,
specifies the resolution and the transition width of the excitation. The sampling
density, Δk, defines where aliased excited spins are localized.
113
Figure 5.1 Schematic illustration of how selectivity in the image domain depends upon the
dimension of excitation k-space. a: A sinc RF excitation pulse with a unidirectional slice
selection gradient along z. b: k-space trajectory traversed by the slice selection gradients while
playing the RF pulse. c: Excited region of the phantom (slice), shown in blue. Using only a
slice selection gradient results in selectivity only in the z dimension in the image domain.
The selective excitation can be extended into two dimensions by extending the
k-space locations to be traversed into two dimensions. In this case, the search space for
k-space locations increases dramatically from a line to a plane. For selectivity in x and
y
dimensions,
 k , k , 0 | k  (k
x
y
x
the
x max
k-space
can
be
defined
as

, k x max ), k y  (k y max , k y max ) . Selective RF pulse design
requires the selection of k-space locations to be traversed with predefined sampling
density, k-space extent, maximum gradient strength, gradient slew rate and RF pulse
length requirements. Just as for the case of traversing 2D imaging k-space in one TR,
114
echo planar, constant angular rate spirals and variable density spirals can be used for
traversing 2D excitation k-space for selective excitation. Constant angular rate spirals
were first demonstrated for 2D selective excitations using the k-space formalism (69).
By traversing the center of the k-space at the end of the RF pulse and weighting the
k-space symmetrically, the excited volume is automatically refocused. Figure 5.2
demonstrates one example of a selective 2D spiral-in k-space trajectory, its
corresponding gradients, and the designed RF pulse (77) intended for selective
excitation of a rectangular region of interest in the middle of a phantom. Since
excitation k-space covers only two dimensions, there is no z-axis selectivity as can be
seen in Figure 5.2d.
The addition of a kz dimension to two dimensional k-space enables three
dimensional selective RF excitation. However, selecting and traversing k-space
locations within three dimensional k-space increases the RF pulse length extensively,
due to the gradient limits imposed by the system as well as peripheral nerve
stimulation limits. Depending on the application requirements, various types of three
dimensional k-space trajectories have been proposed. A stack of spirals (Figure 5.3a)
approach was used for selective inversion recovery pulses for coronary artery imaging
(110) and reduction of susceptibility artifacts in functional MRI (70). Long RF pulse
lengths (in the order of ~20ms) as well as inadequate resolution along the z-direction
hamper the practical application of the abovementioned k-space trajectories.
115
Figure 5.2 An example of 2D spiral RF pulse design. Gradient waveforms (a) are used to
traverse excitation k-space (c). The calculated RF pulse (b) results in selective rectangular
excitation (d) within the x-y plane. However, there is no selectivity in the z-dimension.
The first method to decrease pulse length and increase excitation resolution in
2D RF pulses used multiple shot RF pulse excitations (111,112), and summed
complex images from individual RF excitations yield a final image with full effective
selectivity. This approach takes advantage of the linearity of the STA approximation
(69). Following a similar approach, multi-shot 3D stack of spiral RF pulses were
implemented, resulting in high resolution selective RF excitations with 4 shots of 40
ms RF pulses (113) with an extension to variable density stack of spirals (114) (Figure
116
5.3b). Although the multi shot approach decreases the RF pulse duration, it increases
the acquisition time and is not applicable to large flip angle excitation RF pulses
because of different steady state response of the spins for different shots. With the
development of parallel transmission technology (28,29), it was shown that the
duration of spatially-selective multidimensional RF pulses could potentially be
reduced using multiple RF transmission elements. Similar to parallel imaging, parallel
transmission benefits from the individual coil sensitivities and enables the use of
undersampled k-space without compromising excitation fidelity. By choosing
predefined undersampled spiral (28) and echoplanar (29) k-space trajectories, design
and verification of 2D selective RF pulses was successfully demonstrated. Similarly, a
3D shells trajectory was demonstrated for 3D parallel spatially selective RF pulse
aimed at exciting an arbitrarily shaped region of interest in small animal MR-scanners
(31).
Unlike MR signal acquisition, in which underlying image is a priori unknown,
desired excitation pattern in RF excitation design is one of the parameters used in RF
pulse design. This prior knowledge was first used to determine the kx and ky locations
of a echo-volumar k-space trajectory (Figure 5.3c) via collapsing the 3D power
spectrum, calculated via Fourier transform, of desired pattern along the kz dimension
(115). Incorporating the desired excitation profile information into selection of the
k-space trajectory resulted in significantly reduced RF pulse lengths.
117
Figure 5.3 Various k-space trajectories which are used for 3D selective RF excitation using
one transmit channel. a: Stack of spirals k-space trajectory from Ref. (110), Fig. 2. b: Skip-kz
stack of spirals k-space trajectory from Ref. (113), Fig. 1. c: Echo-volumar k-space trajectory
from Ref. (115), Fig. 1. d: Fast kz-(spokes) k-space trajectory from Ref. (27), Fig. 2.
In addition to reduction of susceptibility artifacts and proper selection of the
excitation ROI, selective excitation RF pulses have been used to reduce B1+
inhomogeneity at high magnetic field strengths. B1+ inhomogeneity correction at 3 T
was achieved by adjusting quadratic in-plane spatial variations of the desired
excitation profile (27). Defining B1+ inhomogeneity as quadratic, a few kx-ky locations
were chosen and shown to be enough for B1+ inhomogeneity correction for the brain
at 3 T field strength (27). This approach resulted in a new type of k-space trajectory
118
using a series of amplitude and phase modulated slice-select subpulses along kz and
phase encoding blips along kx-ky (fast-kz or spokes, Figure 5.3d). When B1+
inhomogeneity is more severe and cannot be well estimated by quadratic terms, e.g. at
7 T, more kx-ky locations are required to obtain homogeneous excitation. However,
additional kx-ky locations increase the RF pulse length. Therefore, both the number of
excitation points and kx-ky locations for slice-selective spokes must be carefully
selected such that B1+ inhomogeneity is mitigated while k-space is traversed within an
acceptable duration.
The addition of parallel transmission into k-space trajectory selection enabled
short RF pulse lengths while mitigating the B1+ inhomogeneity at 7 T. An algorithm
enforcing sparsity in the number of kx-ky locations provided an adequate B1+
inhomogeneity mitigation within a specified excitation FOV in the human brain at 7 T
(116). In addition to B1+ inhomogeneity mitigation, complex target excitation patterns
within a slice were achieved using a sparsity-enforced kx-ky location selection method
(38). This method was shown to outperform Fourier-based (115) and inversion-based
(38) k-space location selection methods. Later, sparse k-space location selection was
employed on 2D parallel transmit RF pulse design (73), and joint methods of
designing k-space trajectories and STA RF pulses simultaneously have emerged with
improved excitation accuracy (117,118).
In this work, the sparse selection of k-space locations for 2D parallel RF pulse
design (73) was extended into 3D selective parallel excitation RF pulse design in order
119
to achieve tailored inner-volume excitations on whole body MRI system at 7 T. The
k-space locations of great importance for achieving the desired excitation profile were
selected by the subspace Orthogonal Matching Pursuit (OMP) method (73) and used
to design STA and LTA RF pulses. The subspace OMP method was compared to a
single-step thresholding method in simulations and phantom experiments.
5.3 Material and Methods
5.3.1 Subspace Orthogonal Matching Pursuit Method
This section revisits the subspace OMP method developed and used for 2D
parallel transmit RF pulse design by Chen et al. (73). In this work, the subspace OMP
method (119) was used to select the most important k-space locations for sparse
parallel transmit 3D RF pulse design.
Theoretical results in sparse signal approximation (120-122) and the
Compressed Sensing method (123) for faster imaging by sparsifying imaging k-space
inspired sparsifying excitation k-space with the addition of parallel transmission
(38,73). By following the notation in Chapter 2, STA parallel transmission RF pulse
design in Cartesian Nyquist sampled k-space can be described in matrix notation,
neglecting the local off-resonance by:
L
m des  c  Dl Ab l
[5.5]
l 1
where c  itM 0 is a constant term assuming initial magnetization, M0, is constant
over the desired excitation profile mdes, Dl  diag{Sl (rs )} is a diagonal matrix
120
containing samples of the sensitivity pattern of coil l, bl is the RF pulse waveform of
coil l, and A is the Fourier Transform matrix, where aij  e
iri k j
is the Fourier basis
function for the jth Nyquist k-space location. The goal of sparse RF / k-space joint
design is to find the fewest k-space locations that can represent the desired excitation
profile mdes within the specified excitation error tolerance.
A sparse approximation of the design problem can be approached by solving
the L1-regularized least squares problem (38,122) or by greedy style algorithm
(120,121). Depending on the sparsity of desired excitation profile and coil sensitivity
patterns in the Fourier domain, the number of k-space locations required for a given
excitation error tolerance could be drastically smaller than that required by the Nyquist
theorem. By overcoming the Nyquist limit, tailored inner-volume excitations can be
implemented with reasonable RF pulse lengths (for example, shorter than the sample
T2 decay time).
The subspace OMP method uses a greedy type approach to include the next
k-space location that provides the maximum error reduction between the desired and
actual profiles in every iteration. Details of the subspace OMP method can be found in
Ref. (119). The subspace OMP algorithm for sparse 3D k-space locations selection is
briefly outlined below. In Step 2, the subspace OMP algorithm finds the k-space
location which maximizes the projection of A(k)b to the residual. Until convergence
criteria (Step 6) are met, OMP algorithm continues to add the next k-space location
into the k-space location subset, K.
121
The single-step thresholding method selects all k-space locations in the first
iteration step of subspace OMP algorithm. In Step 2 of the subspace OMP algorithm,
single-step thresholding algorithm chooses nmax k-space locations, from the 3D
Nyquist grid, which have the highest contribution to the desired excitation profile,
mdes, by ordering projections of A(k)b to the residual.
After selecting the k-space locations with subspace OMP and single-step
thresholding methods, k-space trajectories were designed.
122
Algorithm for Subspace OMP algorithm
1. Initialize: n = 1, residual0 = mdes, nmax (maximum allowed k-space locations, to
limit the length of the RF pulse in case defined tolerance "TOL" hasn't met)
and TOL are given
2. Find the next best k-space location which minimizes the norm between residual
and RF weights b of size1 x Nc :
kn 
arg min
k 3D Nyquist Grid
 residual
n 1
 A(k )b
2
 for any complex b. Here A(k) is the
Ns x L transmit sensitivity weighted Fourier harmonics generated by k :
A (k )  [ S1  e ik r ,..., S L  e ik r ]
3. Add new k-space location to previously chosen k-space location subset
Κ n 1  k1 , k 2 , k n 1
4. Design the n x L size complex RF weights bn using least squares RF pulse

design with Kn and mdes: b n  arg min m des  A(K n )b
b
5. Calculate the residual: residualn  m des  A(K n )b n
6. if residualn
7.
2
 TOL or n  nmax then
n = n+1; go to Step 2
8. else
9.
return Kn with success
123
2

5.3.2 k-space Trajectory Design
After the k-space locations for the desired excitation and coil transmit
sensitivity profiles in 3D k-space is determined, a time ordered k-space trajectory
needs to be defined in order to design 3D selective parallel excitation RF pulse. There
are many options on the selection of k-location order. The goal is to minimize the time
needed to traverse the k-space locations. In the presence of local field inhomogeneity,
the ordering of the selected k-space locations critically affects excitation accuracy. For
example, visiting k-space center last results in automatically refocused excitations in
the case of symmetrically weighted k-space (69). Even though the selected k-locations
do not impose symmetry, center of the k-space should be traversed last to ensure
minimum effect due to dephasing and decay of the central k-space components.
Determination of time-ordered k-space locations was achieved by connecting
selected k-space locations either in a suboptimal EPI-like manner or using a genetic
algorithm (124) framed as a modified traveling salesman problem. Specifically, the
traveling salesman problem was modified such that central k-space locations were
sampled last and the distance between two locations was defined as the Euclidean
distance in 3D space. Both ordering methods were restricted such that each k-space
location was visited exactly once. The genetic algorithm was initialized with 60
population size and limited to1000 iterations.
Gradients have inherent maximum amplitude and slew rate limitations. Using
the gradient constraints of maximum amplitude of 40 mT / m and slew rate of
124
120 mT / m / s, gradient waveforms were designed for the chosen k-space locations
ordering based on the method for designing time-optimal gradient waveforms (125).
After designing the gradient waveforms for both k-space location ordering methods,
the shortest length trajectory was chosen for 3D selective excitation RF pulse design.
For fair comparison of subspace OMP and single-step thresholding k-space location
selection methods, the number of selected k-space locations, nmax, is altered for
matching the k-space trajectory lengths of both methods.
5.3.3 Selective Excitation RF Pulse Design
Using the calculated 3D k-space trajectories and desired excitation profile,
parallel excitation RF pulses were designed in STA and LTA regimes. In order to
design in STA regime, the spatial domain parallel RF design method (34), as
explained in Section 1.3.3, was used. Since calculated k-space trajectories do not obey
the linear class assumptions, direct calculation of the RF pulses using LCLTA method
(76) is not feasible. Therefore, the additive angle method (42) was employed for
calculating LTA RF pulses.
Following the notation of Section 1.3.3 and neglecting the local off-resonance,
excited flip angle pattern, θ(r), of the STA RF pulse can be written similar to Eq. [1.7]
as:
 (r )e
iM xy ( r )
L
Nt
l 1
j 1
 it  Sl (r ) bl (t j )e
125
irk ( t j )
[5.6]
where M xy (r ) is the phase of the transverse magnetization at spatial location r. The
additive angle method includes iterative updates to designed RF pulse and is
initialized by the STA pulse b1 , b 2 ,, b L  . Differences between the desired flip
angle, θdes, and the flip angle pattern resulting from Bloch simulation (78) of RF pulse
b1 , b2 ,, b L  , θ, are used to design a new STA RF pulse
b , b ,, b  using the
1
2
L
following cost function:
 (b 1 ,..., b R ) 

where d new (r ) [ des (r )   (r )]  e
L
2
L
2
2
l 1
2
 Dl Ab l  d new   bl  b l
l 1
iM xy ( r )
[5.7]
. Adding the phase term into dnew ensures that

the flip angle produced by the calculated pulses b 1 , b 2 ,, b L


will add with the
proper sign. Next iteration will start with the pulses b1  b 1 , b2  b 2 ,, b L  b L
 and
the process continues until excitation accuracy stops improving.
5.3.4 Experimental Setup
Experiments were performed on a Siemens whole body 7 T Magnetom scanner
(Erlangen, Germany) equipped with an eight-channel parallel transmit system. An
eight-channel stripline coil array and 7.3-L cylindrical water phantom shown in Figure
1.3 was used in experiments.
126
Figure 5.4 B1+ distribution of the individual elements. a: Axial B1+ amplitude map for each
element of the array. b: Sagittal B1+ amplitude map of transmit channel 2. c: Axial B1+ phase
map for each element of the array. d: Axial B1+ phase map of transmit channel 2.
Multi-slice acquisition for B1+ calibration was performed following the method
described in Ref. (79) and explained in Section 1.3.6. In Figure 5.4a,c, measured
individual channel B1+ magnitude and phase maps are shown in the axial plane
through the isocenter. One representative sagittal B1+ magnitude and phase map of
transmit coil 2 is shown in Figure 5.4b,d. The following imaging parameters were
used in B1+ calibration: FOV = 260 x 260 mm2, echo time (TE) = 1.99 ms, acquisition
matrix = 96 x 96, number of slices = 21, and slice thickness = 8 mm. Total acquisition
time for B1+ profiles in all eight channels was 357 s. ΔB0 was measured using the
phase information from two multi slice GRE images with different TE values
127
(TE1 / TE2 = 5.1 / 4.08 ms) and was incorporated into RF pulse design to compensate
for the phase accrual due to main magnetic field inhomogeneity.
The spatial domain parallel RF design (34) and additive angle method (42)
were used to design parallel RF pulses with a 20° and 90° target flip angle,
respectively. The target excitation flip angle distribution θdes was a homogenous 4 x 2
x 2 cm3 rectangular box profile with axial distribution blurred by convolving with a
Gaussian kernel of FWHM = 1.2 cm to reduce ringing artifacts in the resulting
magnetization distribution. 3D k-space was undersampled by a factor of two to help
both algorithms extend coverage of the outer regions of excitation k-space. In addition
to undersampling k-space, slice resolution of the B1+ maps was reduced from 96 x 96
to 33 x 33 for managing computational cost of k-space locations selection step
efficiently.
Designed RF pulses were simulated using Bloch simulator. Excitation profiles
of RF pulses designed with k-space trajectories calculated from subspace OMP and
single-step thresholding method were compared using NRMSE of the magnetization
and RMSE of the flip angle for STA and LTA designs, respectively. Multi-slice flip
angle profiles of the designed RF pulses were measured using the B1+ calibration
technique (specifically, designed parallel RF pulses were played as saturation pulses
followed by a multishot segmented turbo FLASH acquisition with 2 segments).
Imaging parameters were: FOV = 260 x 260 mm2 TE = 1.97 ms, acquisition matrix =
128 x 128, acquisition time = 168 s, number of slices = 21, and slice thickness = 8
128
mm. In addition to flip angle maps, 3D spoiled GRE using calculated RF pulses as
excitation pulse were acquired for comparing excitation fidelity of both k-space
location selection methods. Longer TRs were used for designed LTA RF pulses in
order to decrease the saturation effects on the excitation profile. The following GRE
imaging parameters were used: FOV = 260 x 260 mm2, TR = 50 ms for STA / 300 ms
for LTA, TE = 7.9 ms, acquisition matrix = 256 x 256 for STA / 128 x 128 for LTA,
number of slices = 48, and slice thickness = 5 mm. During GRE image acquisition, the
net power deposition of designed RF pulses was measured using the power monitoring
setup described in Section 1.3.6.
Figure 5.5 Distribution of the selected k-space locations for both algorithms.
129
5.4 Results
5.4.1 k-space Trajectory
Selected k-space locations for OMP and single-step thresholding methods are
shown in Figure 5.5 by projecting the 3D k-space along the axis dimensions. Use of
subspace OMP method for selection of the k-space locations resulted in larger k-space
coverage compared to single-step thresholding method. By calculating the
time-optimal gradient waveforms, k-space trajectories that obeyed the system
maximum gradient and slew rates were defined. In Figure 5.6, blue dots represent the
selected k-space locations and red lines represent the designed k-space trajectory. 120
and 200 k-space locations were selected to approximately match RF pulse lengths of
the subspace OMP (8.78ms) and single-step thresholding (8.65ms) methods. These
pulses correspond to ~35 times reduction of the fully sampled 3D Cartesian k-space
trajectory length.
130
Figure 5.6 Designed k-space trajectories for subspace OMP method and single-step
thresholding method
Figure 5.7 Experimental flip angle profiles of designed LTA RF pulses using k-space
trajectories designed with subspace OMP and single-step thresholding method.
131
5.4.2 Experiments
Using designed k-space trajectories (Figure 5.6), selective excitation parallel
RF pulses were designed for STA and LTA regimes. Prior to experimental application
of the calculated RF pulses, Bloch simulation results of both k-space location selection
methods were compared. According to Bloch simulations, the extension of k-space
coverage achieved with the subspace OMP method resulted in reduced error:
NRMSE / RMSE = 0.011 / 0.26 (subspace OMP), 0.013 / 0.34 (single-step
thresholding).
Figure 5.8 Axial and sagittal GRE images acquired using designed STA (a) and LTA (b)
selective excitation parallel RF pulses. The red circle and rectangle indicates the boundaries of
the phantom.
The flip angle profiles of designed RF pulses were verified in experiments.
Figure 5.7 shows the axial / sagittal flip angle maps of LTA RF pulses designed using
k-space trajectories obtained from subspace OMP and single-step thresholding
132
methods. Experimental flip angle profiles verified that the subspace OMP method
resulted in higher fidelity flip angle distributions compared to the single-step
thresholding method, especially in the axial flip angle distributions.
The axial and sagittal experimental MR signal profiles obtained from subspace
OMP versus the single-step thresholding method are shown in Figure 5.8 a and b for
STA and LTA, respectively. As the excitation flip angle increases, excitations on
undesired locations (where desired excitation flip angle is 0) becomes more
pronounced. Improved STA excitation fidelity of the RF pulse associated with klocations selection with subspace OMP method was also associated with a slight
increase in net power deposition (~0.9W compared to ~0.8W for single-step
thresholding). However, the power deposition behavior was reversed for the LTA
case: ~34W for OMP and ~47W for thresholding.
5.5 Discussion
Feasibility of inner-volume excitations with good selectivity was demonstrated
on a whole-body 7T scanner using an eight channel parallel transmit system.
Reasonable RF excitation pulse lengths (~8.7 ms) were realized using multiple
transmit elements and sparse subselection of k-space locations by subspace OMP in
one case and single-step thresholding method in another case. These sparse k-space
trajectories represent ~35 times reduction in RF pulse lengths compared to fully
sampled 3D Cartesian k-space trajectories. This enabled acceleration beyond the limits
of conventional parallel transmission with eight elements, while preserving acceptable
133
excitation profiles. Calculation time to determine k-space locations was greater for the
subspace OMP algorithm since the duration of each sparsifying iteration is
approximately equivalent to the overall duration of the single-step thresholding
approach.
By using the calculated k-space trajectories, flip angle maps and GRE images
using LTA parallel RF pulses were demonstrated, even though the k-space formalism
is only valid in the STA regime as explained in the section 5.2.1. In other words, the
applied k-space trajectories are not necessarily optimal for LTA RF pulse design, but
can still be used to design LTA RF pulses with reasonable inner-volume excitations.
Imperfections in the excitation profile were more pronounced at the locations where
the desired flip angle is zero especially for the LTA RF pulse design. These
imperfections could stem from gradient imperfections, eddy current effects and local
main field inhomogeneities. Some of these effects can be measured, e.g. with field
monitoring (126), and corrected for in RF pulse design in the STA regime (39). The
inability to perfectly null outer volumes with inner-volume excitations is one of the
main limitations of reduced FOV imaging, since excited regions outside of the reduced
FOV will fold into the region of interest. It was shown that parallel imaging
techniques in addition to 2D parallel RF excitation can be used to overcome this
difficulty (127). Future work will incorporate parallel imaging methods into 3D inner
volume excitations in order to overcome unwanted aliasing from excited locations
outside the region of interest.
134
5.6 Acknowledgements for Chapter 5
I would like to thank Dr. Dong Chen for his help and collaboration on the
subspace OMP method. Dr. Hans-Peter Fautz from Siemens Medical Solutions in
Erlangen, Germany is acknowledged for collaboration on the flip angle mapping
sequence.
135
CONCLUSION
The need for higher SNR and higher acquisition speeds will continue to drive
demand for UHF-MRI in the future. Nevertheless, many technical challenges remain
to be overcome. The inhomogeneity of the traditionally generated B1+ field and, more
importantly, the increase in SAR per unit flip angle are significant challenges which
continue to obstruct or at least complicate the diagnostic usage of UHF-MRI. These
challenges have forced the MR community to go beyond traditional low-field
approaches and to research new possibilities. Parallel RF excitation techniques offer
significant relieve of UHF challenges by enabling decreases in B1+ inhomogeneity and
SAR. However, parallel RF excitation is a developing technique and continued
progress will be required in order to fully explore the potential of UHF-MRI for
clinical diagnosis.
In this thesis we studied B1+ field behavior and global SAR interactions in the
parallel RF excitation from a systematic perspective. We developed methods to
incorporate measured subject-specific E field interactions into parallel RF excitation
pulse design and RF shimming in order to reduce SAR while maintaining excitation
fidelity. We showed that including E field interactions results in lower global SAR in
phantom
and
in
vivo
studies
while
maintaining
/
improving
the
B1+
fidelity / homogeneity. Additionally, we demonstrated the quantitative SNR benefits
of UHF-MRI systems in vivo using developed RF excitation methods. For MR system
monitoring, we proposed a pre-scan-based power calibration technique to estimate
136
subject-specific individual channel power properties of a parallel transmission MRI
system. The proposed technique was used successfully to design parallel RF excitation
pulses obeying strict power limits of the MR system, such as peak and average power.
The importance of coil-subject setup increases at UHF due to SAR concerns. We
analyzed the RF power requirements and SAR of parallel RF excitation systems as a
function of the distance between the transmit coil array and the subject in simulations.
It was found that there are SAR benefits in moving transmit coils away from the
subject. In the last chapter, we utilized the sparse selection of k-space trajectories in
order to design parallel RF excitation pulses for inner-volume excitation. We
demonstrated the feasibility of inner-volume excitations with reasonable RF pulse
lengths in phantom studies.
Recommendations for future work
In this work we demonstrated the benefits of including measurable E field
interactions in parallel RF excitation. The pre-scan power calibration step accounting
for E field interactions uses a power measurement system which includes RF power
sensors and directional couplers. The accuracy of calibration and tracking is expected
to improve as the measurement system is moved closer to the subject. In our current
power measurement setup calibrated E field interactions overestimate the SAR in the
subject. An improved power measurement system could be located close to the
transmit coils, but this improvement could be quite challenging given the need to
operate in the presence of high magnetic fields. A power sensing approach with
137
directional couplers fed into MR receivers was shown to be able to detect changes in
the play out of predefined RF pulses (65). Similar MR receiver based power sensing
apparatus could be used to better estimate SAR inside the subject.
The proposed maximum efficiency RF shimming aims to increase
homogeneity while decreasing RF power deposition in small ROIs for local RF
shimming. The method could be extended to enable homogeneous excitations in larger
ROIs by imposing additional constraints on homogeneity in the calculation of the RF
shimming weights. This may require a different algorithm to find the associated
coefficients.
The capability to predict individual channel forward and reflected power in
parallel RF transmission systems can be used further in parallel RF excitation pulse
design in order to minimize reflected power. Decrease in the reflected power is
desirable from a system perspective since it allows power amplifiers to deliver power
to the transmit coils more efficiently. For the tracking of global SAR as well as
forward and reflected power, separate power measurement systems - one close to the
coils and another at the output of the power amplifiers - may be desirable.
Inner-volume excitations are valuable at UHF as they offer the potential to
reduce image acquisition time or increase spatial resolution over reduced field of view.
Yet, reduced FOV imaging is challenging due to system and B1+ calibration
imperfections, as well as RF pulse design techniques which result in incomplete
suppression of the unexcited regions. Signal from imperfectly suppressed regions can
138
alias into a target reduced FOV and result in significant image artifacts. Reduced FOV
imaging may benefit from combining inner volume excitations with compressed
sensing (128) methods to overcome these problems. In addition, the size of the
excitation profile has been shown to affect the SAR consequences of parallel RF
excitation pulses (51). It would be beneficial for UHF-MRI to investigate the SAR
consequences of inner-volume excitations and, more importantly, to compare with
conventional RF excitation pulses, such as slab selective sinc pulses.
Power prediction and monitoring techniques have been used extensively during
the course of this thesis. Such techniques have been used to decrease global SAR and
to design RF pulse designs conforming to safety limits as well as strict operational
limits of RF power amplifiers. An extension of the global SAR prediction techniques
described here has been shown to enable prediction of the local SAR consequences of
any parallel RF excitation pulse (62,63). The techniques described in this thesis will
also be applicable for local SAR management, which will further enable exploration
and maximization of the benefits of UHF MRI.
139
APPENDIX
Parallel transmission experiments require knowledge of the B1+ distributions of
individual coil transmit elements in order to tailor the RF excitation as desired. In
addition to B1+ distributions, B0 maps and, if needed, power correlation matrices must
be measured / calibrated before designing parallel transmission RF pulses. Even after
scanner-related-measurements are acquired, RF pulse design requires inputs such as
the desired excitation profile, the choice of RF pulse design method, the excitation kspace trajectory and so on. Since parallel transmit systems are still in the development
stage, the workflow of obtaining the abovementioned inputs and designing parallel
transmission RF pulses is not yet supported with intuitive graphical user interfaces
(GUIs) of the sort used in clinical MRI scans. The lack of application specific GUIs
for parallel transmit systems results in inefficiencies in the MRI scan workflow, e.g.
longer experiments and operator errors. In order to increase the efficiency and
accuracy of parallel transmit experiments, we developed and used custom-designed
GUIs in the Matlab programming environment in the course of this thesis. These GUIs
can be used not only for parallel transmit experiments but also for transmit coil design
(e.g. using electromagnetic simulation results as inputs to test the suitability of
prospective coil designs) and for educational purposes (e.g. for practice in RF pulse
design). The GUIs described here have been made available for download using the
following web link: http://www.cemnaz.com/~cem/projects/GUI. In this appendix, we
140
describe the workflow of parallel transmit experiments with the guidance of the
developed GUIs.
A.1 RF Shimming GUI
An RF shimming GUI was developed for and used in the maximum efficiency
RF shimming study described in Chapter 2. Figure A.1 shows the workflow of the RF
shimming experiment with numbers in parentheses indicating corresponding locations
in the GUI that can be found in Figure A.2.
B1+ distributions of individual transmit channels can be visualized inside the
GUI after including them from either MR images obtained with turbo FLASH based
flip angle mapping techniques as described in Section 1.3.6 or Matlab .mat files which
contain flip angle information from any imaging method or simulation. Using a data
cursor, flip angles inside figures can be displayed and, if needed, a colorbar can be
included with any figure within the GUI.
RF shimming requires a desired shimming ROI to be defined. Four different
ROI selection mechanisms are implemented as shown in the Shim ROI Select panel
(Figure A.2-2). The shimming ROI can be interactively selected from an additional
MR image or an image obtained with sum of squares (SoS) combination of the B1+
profiles. Additionally, the shimming ROI can be defined as the whole sample or
incorporated from a saved .mat file. After choosing the shimming ROI, the user needs
to specify the coils to be used in RF shimming weights calculation. Initially all eight
coils (the maximal coil set of our 8-channel parallel transmit system) are pre-selected.
141
The user can choose any subset of transmit coils by using check boxes and for
convenience odd and even coils can be selected easily by pressing the corresponding
button from the Select channels panel (Figure A.2-3).
Four different RF shimming methods were implemented in the current GUI.
Two of them are amplitude and phase RF shimming methods indicated by the
RF Shim panel (Figure A.2-4a) and the rest are phase only RF shimming methods
indicated by the Phase Only RF Shim panel (Figure A.2-4b). Push buttons (Figure
A.2-4) initiate calculation of the RF shimming values aiming to match the shim ROI
defined in Figure A.2-2. Pushing the Calculate Shim button calculates RF shimming
weights using a regularization parameter, and if available, the Φ-matrix as explained
in Section 1.3.4 using Eq. [1.14]. When only the magnitude of the shim profile is
targeted, whim weights are calculated by an iterative search algorithm using Matlab's
fminsearch function. Results of both methods are shown in Figure A.2-5. Maximum Tx
Efficiency button calculates the maximum and minimum transmit efficiency RF
shimming values as described in Section 2.3.1. The No Amplitude Target button
calculates unit amplitude phase only shim weights aiming to align the phases of the
transmit elements inside the chosen ROI. In this type of RF shimming the amplitude
of the ROI is not considered but uniform phase distribution is targeted. We
successfully used this shimming approach to obtain Birdcage-type profiles by
prescribing a small ROI at the center of the phantom on a transmit array with
azimuthally distributed individual elements. The With Amplitude Target button
142
calculates the unit amplitude RF shimming weights aiming to match only the
amplitude of the shim ROI. Both Phase Only RF Shim panel algorithms use iterative
search algorithms employing Matlab's fminsearch function. Transmit efficiencies of
the calculated RF shimming weights aligned with minimum and maximum possible
transmit efficiencies are displayed in the Transmit Efficiency panel.
Changing the amplitude and phase of calculated RF shimming weights, which
are displayed in Figure A.2-5, automatically updates the displayed RF shimming
results and transmit efficiency metrics. This feature enables interactive changes to the
calculated RF shimming weights, with immediate visualization. This helps users to
understand the phase and amplitude relationships in a multi-channel transmit system.
If those changes result in unsatisfactory results, the user can press the Go to Original
Shim button to recover previously calculated RF shimming weights. Additionally, RF
shimming weights can be saved to any folder by using the Save to .txt button.
Bloch simulations for adiabatic RF pulses were used in Section 2.3.3 in order
to compare RF power benefits of using the maximum transmit efficiency RF
shimming method (Chapter 3). Choosing an adiabatic RF pulse using Choose RF from
.mat button in Figure A.2-6 enables the Bloch Simulations for Adiabatic RF Pulse
panel. This panel can be used to run Bloch simulations of the chosen adiabatic RF
pulse with the specified maximum voltage. An image of z-magnetization in the sample
resulting from Bloch simulations is shown in Figure A.2-6 with the mean and standard
deviation of the z-magnetization. The frequency response of the adiabatic RF pulse for
143
the given voltage is displayed for the weakest B1+ spatial location with an additional
plot in order to determine whether the adiabatic condition over the ROI is met or not.
In Section 2.3.3, the adiabatic condition in the sample was met by increasing or
decreasing the maximum RF voltage and checking the Bloch simulation results
interactively. Peak and mean power of the RF pulse is predicted and displayed by
including a power correlation matrix, Φ, with the defined calibration voltage.
144
Obtain B1+ distribution and add to GUI from (1)
an MR experiment (1a)
a simulation (1b)
Select targeted RF shimming ROI (2) from
an MR
image
the whole
sample
an image obtained with SoS
combination of B1+
a saved .mat file
Select channels to be used in RF shimming (3)
Select type of the RF shimming method to be used (4)
Magnitude and phase RF shimming (4a) Phase only RF shimming (4b)
• Maximum efficiency RF shimming
• Aiming to align only the phases of
(Section 2.3.1)
transmit elements
• RF shimming aiming target
• Aiming to align phases and match the
distribution (Section 1.3.4)
uniform amplitude distribution
Visualize and change the calculated RF shimming values (5)
Bloch simulations, if needed, for an RF pulse to obtain frequency response (6)
Use calculated RF shimming coefficients in experiments
Figure A.1 Workflow of an RF shimming experiment. Relation to the RF shimming GUI is
indicated by the numbers in parentheses.
145
146
Figure A.2 Screenshot of RF Shimming GUI
A.2 Parallel Transmit GUI
A parallel transmit GUI was developed and used for the work reported in
various chapters of the thesis. Figure A.3 shows the workflow of a parallel
transmission experiment with the numbers in the parentheses indicating corresponding
locations in the GUI that can be found in Figure A.4.
B1+ distributions of individual transmit channels can be visualized inside the
GUI after including them from either MR images obtained with turbo FLASH based
flip angle mapping technique as described in section 1.3.6 or .mat files which contain
flip angle information from any imaging method or simulations. Parallel transmission
requires desired excitation profile to be defined. Three different ROI selection
mechanisms are implemented as shown in the Desired Profile Selection panel (Figure
A.4-2). The desired excitation profile can be selected interactively from an image
obtained with sum of squares (SoS) combination of the B1+ profiles. Additionally, the
desired excitation profile can be defined as the whole sample or incorporated from a
saved .mat file. After choosing the desired excitation profile, the user must specify the
coils to be used in parallel transmission RF pulse calculation. Initially all eight coils
are pre-selected. As for RF shimming, the user can choose any subset of transmit coils
by using check boxes and for convenience odd and even coils can be selected easily by
pressing the corresponding button from the Select channels panel (Figure A.4-4). Main
magnetic field inhomogeneities can be included in RF pulse design using the B0 Map
panel in Figure 1.1-3 by including a predefined .mat file or by first choosing names of
147
two GRE images with different TEs from a pop-up menu and then pushing the
Calculate B0 Map button.
Within the pTx Pulse Info panel, the k-space Trajectory panel enables users to
choose the type of excitation k-space trajectory for RF pulse design. Three different
k-space trajectories are implemented:
1. Constant Density Spiral
2. Variable Density Spiral
3. EPI like (Echo Planar)
Constant density spirals were used in Chapters 1 & 3 and variable density
spirals were used in Chapter 1. EPI-like trajectories were not incorporated in RF pulse
design in the thesis, but were implemented in the GUI since they provide a useful
educational perspective for accelerated excitations. Changing parameters in the GUI,
such as excitation resolution, excitation field of view and acceleration, enables
automatic calculation and display of the selected type of k-space trajectory. k-space
trajectory calculation aims for the shortest possible RF pulse length while obeying
gradient specifications defined in the GUI. Additionally, the RF pulse length for the
calculated k-space trajectory is displayed in the k-space Trajectory panel.
Three different RF pulse calculation algorithms are implemented and shown in
the Pulse Design Type panel (Figure A.4-6). Depending on the type of solution, they
are classified as regularized and not regularized. Regularization based RF pulse
designs are implemented in STA and LTA regime. On the other hand, strict constraint
148
RF pulse design (not regularized) is implemented only in the STA regime. Regularized
RF pulse design methods and strict constraint RF pulse design methods were used in
Chapter 1 and 3, respectively. For constrained RF pulse design, the user must choose a
constraint type from the Constraints panel. All options include peak and average
forward and reflected power constraints and global SAR constraints as defined in the
Power Constraints panel. The power correlation matrix must be imported, using the
Include PHI button, for accurate power prediction which is essential in constrained RF
pulse design. Additional parameters for RF pulse design e.g. flip angle, smoothing
profile, and regularization parameter, can be included from Figure A.4-7. After all the
parameters are selected the RF pulse will be designed and displayed in Figure A.4-8
after pushing the Calculate RF Pulse button. Relevant information such as NRMSE
and number of iterations (e.g. conjugate gradient iterations) used in pulse design is
displayed under the amplitude of the designed RF pulse. Calculated RF pulse can be
exported to different formats which can be used in the MR scanner. Write In Float
button generates .float files of individual channel RF pulses and gradients, then puts
them in an ".Output/RFPulses" directory with separate folder names for each
individual transmit channel (TX1-TX8). The WriteIn_pTXRFPulse button generates
the 'pTXRFPulse0.ini' file under the directory ".Output/RFPulses". All variables inside
the GUI can be saved for future reference using the Save Variables button.
149
Obtain B1+ distribution and add to GUI from (1)
an MR experiment (1a)
a simulation (1b)
Select the desired excitation profile (2) from
an image obtained with SoS
combination of B1+
a saved .mat file
the whole sample
Include the B0 map (3) from
two GRE MR images
precalculated .mat file
Select channels to be used in pTx experiment (5)
Select type of the excitation k-space to be used (4)
Constant Density Spiral
Variable Density Spiral
EPI
Select type of RF pulse design method (6)
Using regularization (Chapter 1 )
• STA
• LCLTA
Without using regularization (STA, Chapter 3)
• Unconstrained
• Only global SAR constrained
• Constrained
Define additional parameters for RF pulse design (7)
Calculated RF pulses and Bloch simulation results are shown in (8)
Figure A.3 Workflow of a parallel transmission experiment. Relations to the parallel
transmission GUI are given by the numbers in parentheses.
150
151
Figure A.4 Screenshot of Parallel Transmit GUI
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