MR Radar: Parallel Radiofrequency Transmission in Principle and Practice

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 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, , 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] is the electrical conductivity, E(r, pt )   bl ( pt )el (r ) is the superposition L where 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 where b pt  b1, pt  b L , pt  is the concatenation of the RF pulse waveforms, T 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  t ( pt ) Nt 1 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: M (r, T )  i M 0 (r ) Sl (r)  bl (t )eiB0 (r )(t T ) eirk (t ) dt where L T l 1 0 [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 k (t )    G ( )d is the excitation k-space trajectory, defined as the time reversed T 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:  (r )    S (r )  bl* (t )eiB (r )(t T ) eirk (t ) dt T L 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  Cfullb*full , where Cfull  C1  CL  , and Cl is a Ns x Nt system matrix with elements cij  tSl* (r j )e Given a desired flip angle distribution, des,  iB0 ( ri )( t j T )  iri k ( t j ) e . and a chosen k-space trajectory, parallel pulse waveforms can be calculated by solving the minimization problem: bˆ full  arg min{ Cfullb*full  b*full 2 des 2  R(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 Φfullbfull RSTA (bfull )   bfull [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: Sdes (r)   wl Sl (r) L l 1 [1.12] 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  L 2  2 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: ˆ  arg min{ Sw  S des 2  R(w )} w 2 [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 ( = 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 des (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 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 I 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: B1 (r)   w( n)b( n) (r) and E(r)   w( n )e( n ) (r) N N n 1 n 1 [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 where E(r ) 2 dv  w H Φw 2 [2.3] 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, , 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, 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 can be accomplished using various numerical optimization algorithms. However, it can be shown that calculating the maximum and minimum of 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, ≈ 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 ( ) B C 27.0° 23.4° 30.7° D 9.0° A B C 28.0° 23.9° 30.8° Volunteer 4 D 7.6° A 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 6.58 7.51 6.51 ± ± 9.96 ± 9.23 ± ± ± ± ± 4.8° 12.0° 9.4° 13.9° 3.3° 1.83 9.22 RF Power Deposition C ± 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 Body Dimensions (cm)* 1 Volunteer 1 ‖ ‖ 1 Volunteer 2 2 73 216.3° ‖ ‖ 0.44 0.76 273.4° Volunteer 3 1 Volunteer 4 1 3 4 31.3° ‖ ‖ 0.45 0.6° ‖ ‖ 0.71 17.7° 1 342.7° 316.0° 0.5 45.2° 0.77 1.59° 0.45 92.1° 0.67 ∡ ∡ ∡ ∡ A to C P to C L to C R 0° 7.1 10.8 7.6 2.1 0.36 0° 7.6 9.6 8.9 2.5 345.6° 0.57 0° 8.9 12.1 12.6 2.0 348.1° 0.61 0° 7.7 12.1 12.3 2.2 0.22 * 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 Volunteer 4 2.3 2.8 gain at 7T 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 ( pt )  b Hpt Φlfwd b pt and Prfll ( pt )  bHpt Φlrfl b pt Pfwd [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 b Hpt Φlrfl b pt  Prfll , peak , l  1, , L l   b Hpt Φlfwd b pt  Pfwd , ave , l  1,  , L [3.2] [3.3] [3.4] p   b Hpt Φlrfl b pt  Prfll ,ave , l  1,, L [3.5] 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 such that b H Φ b  globalSARLimit full full full l b Hpt Φlfwd b pt  Pfwd , peak b Hpt Φlrfl b pt  Prfll , peak 2 2 l , p l , p l   b Hpt Φlfwd b pt  Pfwd l , ave   b Hpt Φlrfl b pt  Prfll ,ave p [3.6] l p where b full  b1Tt , b T2 t  b TPt  is the concatenation of the coil RF pulse waveforms T 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 (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 k (t )    G ( )d t [5.2] 0 where G( ) 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 M xy (r )  i M 0  B1 (t )e T  i r  t G ( ) d dt T [5.3] 0 where M0 is the initial magnetization before applying RF. Defining a spatial frequency variable k(t) as k (t )    G ( )d T [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  k , k , 0 | k  (k y dimensions, 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: m des  c  Dl Ab l L l 1 [5.5] 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, (r), of the STA RF pulse can be written similar to Eq. [1.7] as:  (r )e iM xy ( r )  it  Sl (r ) bl (t j )e L Nt l 1 j 1 125 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, des,   using the and the flip angle pattern resulting from Bloch simulation (78) of RF pulse b1 , b2 ,, b L  , , are used to design a new STA RF pulse b 1 , b 2 ,, b L following cost function:  (b 1 ,..., b R )  where d new (r ) [ des (r )   (r )]  e   Dl Ab l  d new   bl  b l L l 1 iM xy ( r ) 2 L 2 2 l 1 2 [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 des 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. 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