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Continuous Wave Nuclear Magnetic Resonance: Estimation of Spin-System Properties from Steady-State Trajectories

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Continuous Wave Nuclear Magnetic Resonance: Estimation of Spin-System Properties from Steady-State Trajectories Continuous wave nuclear magnetic resonance: estimation of spin-system properties from steady-state trajectories James Christopher Korte ORCID: 0000-0001-9152-1319 Ph.D Engineering (351AA) August, 2017 Department of Biomedical Engineering, Melbourne School of Engineering The University of Melbourne Submitted in total fulfilment of the degree of Doctor of Philosophy 2 Abstract Magnetic resonance imaging (MRI) is a powerful imaging modality, widely used in routine clinical practice and as an investigational tool in basic science. The contrast in MRI is related to both the underlying tissue properties, which undergo disease or injury related changes, and to the MRI method and sequence parameters used. It is the latter with which this thesis is concerned: the design and implementation of novel MRI acquisition paradigms and associated reconstruction methods. The majority of MRI methods excite the object of interest with a series of short RF pulses, varying the weaker spatial magnetic field using the gradients, and ensuring the RF transmitter is inactive while acquiring a series of decaying MR signals. This regime linearises the inherently nonlinear behaviour of a magnetic resonance spin-system, allowing the acquired signals to be considered in a spatial frequency space and an image to be reconstructed using the well known Fourier transform. It is our assertion that nonlinear behaviour of the magnetic spin signal will lead to advantageous attributes in future MR methods, just as moving beyond conventional linear spatial gradients to nonlinear encoding fields led to methods for accelerated imaging and variable spatial resolution. Reconstruction of spin-system properties from nonlinear MR signals requires algorithms beyond the Fourier transform. In this thesis we propose spectroscopy, radial projection imaging and re- laxometry methods as optimisation problems which minimise the mismatch between experimental measurements and predictions from Bloch equation based signal models. The use of continuous wave (CW) excitation patterns allows the development of signal models which are computationally efficient as they rely on analytical solutions of the Bloch equations or matrix inversion via harmonic balancing, rather than numerical integration. Ultra-short relaxation methods have been applied to a range of applications and demonstrate that MRI is finding use in areas far beyond traditional soft-tissue imaging. Soft tissues have an easily observable long duration MR signal, whereas the signal decays rapidly for harder tissues such as bone, or in regions that distort the magnetic field due to magnetic susceptibility gradients, such as the lungs. Rabi modulated CW techniques operating in a fully continuous mode have the potential to measure ultra-short relaxation signals in a similar range to `true' zero echo time techniques. Work inspired by quantum optics has shown that exciting a spin-system with a long duration Rabi modulated RF field leads to a significant steady-state MR signal. The steady-state trajectory is highly nonlinear and can be expressed as a series of harmonics of the amplitude modulation fre- quency of the RF field. This harmonic response provides a natural decoupling of the excitation and measurement bandwidth, and the ability to maintain a steady-state response under low power excitation reduces the isolation requirements between hypothetical transmit and receive chains. Our experimental investigation of steady-state trajectories makes use of two pseudo-simultaneous excitation and measurement protocols. Whilst these methods were adequate to explore the proof-of- concept applications, hardware modifications are suggested to unlock the full potential of continuous wave excitation patterns. This thesis demonstrates that CW excitation patterns allow the construction of efficient prediction models and elicit an information-rich steady-state response from which underlying spin-system prop- erties can be reconstructed. It is anticipated that further development of these concepts and related hardware modifications will lead to new continuous wave imaging paradigms. 3 4 Declaration This is to certify that (i) the thesis comprises only their original work towards the Ph.D except where indicated in the preface; (ii) due acknowledgement has been made in the text to all other material used; and (iii) the thesis is fewer than 100,000 words in length, exclusive of tables, maps, bibliographies and appendices. James Korte Date 5 6 Publications The work presented in this thesis has produced the following publications and conference presenta- tions. Journal papers • Korte, J.C., Layton, K.J., Tahayori, B., Farrell, P.M., Moore, S.M. and Johnston, L.A. \NMR spectroscopy using Rabi modulated continuous wave excitation", Biomedical Signal Processing and Control, 2017, 33, p.422-428 Conference abstracts • Korte, J.C., Tahayori, B., Farrell, P.M., Moore, S.M. and Johnston, L.A. \Relaxometry via steady-state ring-locked trajectories", Proceedings of the 25th Annual Meeting of ISMRM, Honolulu, USA, 2017 • Korte, J.C., Tahayori, B., Farrell, P.M., Moore, S.M. and Johnston, L.A. \Rabi Modulated Continuous Wave Imaging", Proceedings of the 24th Annual Meeting of ISMRM, Singapore, 2016 (Power Pitch Presentation) • Korte, J.C., Tahayori, B., Farrell, P.M., Moore, S.M. and Johnston, L.A. \Gapped measure- ment of spin system response to periodic continuous wave excitation", The Australian and New Zealand Magnetic Resonance Society, Bay of Islands, New Zealand, 2015 (Oral Presentation) • Korte, J.C., Layton, K.J., Tahayori, B., Farrell, P.M., Moore, S.M. and Johnston, L.A. \En- coding chemical shift with Rabi modulated continuous wave excitation", Proceedings of the 22nd Annual Meeting of ISMRM, Milan, Italy, 2014 (Oral Presentation) 7 8 Acknowledgments Firstly, I would like to express sincere gratitude to my supervisors for their patient guidance through- out my PhD candidature. Leigh Johnston for the constant enthusiasm and lively debates, Peter Farrell for the confusing but ultimately insightful comments, Bahman Tahayori for his mathemat- ical genius and Stephen Moore for imparting his wide knowledge of parallel computation. I have learnt a great deal from each of you and have no doubt your individual styles of thinking will shape my research in the years to come. Additional thanks to the members of my advisory committee, David Grayden and John Wagner, for keeping my candidature on track and offering perspective and direction. I am very grateful to my friends and colleagues from the Melbourne School of Engineering, the Melbourne Brain Centre Imaging Unit and the Florey Neuroscience Institute: Roger Ordidge, Brad Moffat, Scott Kolbe, Jon Cleary, Sonal Josan, Camille Shanahan, Amanda Ng, Kelvin Layton, David Wright, Yasmin Blunck, Warda Syeda, Paul Bloembergen, Dhafer Alahmari, Eric Wang, Muhammad Hanif, Muhammad Usman Khalid, Rosa Shishegar, Edward Green, Myrte Strik, Julia Neugebauer, Peter Yoo, Annie Shelton, Sanuji Gajamange, Frederique Boonstra, Errol Lloyd and Yamni Mohan. In particular, a big thank you to Kelvin and David for teaching me how to drive the MRI. Yasmin, Warda, Rosa and Ed for all the interesting discussions in our weekly \MRI for idiots" meeting. I have been lucky enough to visit a few labs during my candidature. I learnt a great deal during a one month lab visit with the MRI group in Freiburg, my thanks to J¨urgenHennig, Maxim Zaitsev, Frederik Testud and Sebastian Littin. Thanks to Samuel Patz and Mirko Hrovat for your valuable comments on my experiments and showing me around your laboratory in Boston. I would also like to thank Steffen Bollmann and the Centre for Advance Imaging in Queensland for your feedback on my work. To my friends for reminding me there is more to life than research. Thanks for all the Friday night sessions at E55 to vent some frustration when things are not going to plan, for helping me stay active with great company on hiking and climbing trips and keeping me sharp with the occasional acoustic rap battle. My family is a great source of inspiration, I would like to thank my parents Chris and Katherine for instilling in me the importance of knowledge and supporting my scientific curiosity. To my sisters for teaching and challenging me; Laura for introducing me to scepticism and debate, Anna for reminding me intelligence has many forms. Lastly, I'd like to thank all the medical professionals who have patched me up over the years and continue to inspire me to pursue research in a health related field. 9 10 Contents 1 Introduction 17 2 Theory 23 2.1 Introduction . 23 2.2 Spin Physics . 24 2.2.1 Single atomic particle . 24 2.2.2 Ensemble of atomic particles . 27 2.3 Bloch equations . 30 2.3.1 Steady-state solutions . 32 2.3.2 Pulse excitation solutions . 38 2.4 Measurement Concepts . 41 2.4.1 Signal detection . 41 2.4.2 Signal formation . 42 2.4.3 NMR spectroscopy . 47 2.4.4 NMR relaxometry . 48 2.5 Imaging Concepts . 51 2.5.1 Slice selection . 51 2.5.2 Spatial encoding . 53 Appendices . 59 2.A Bloch equations in the rotating frame . 59 2.B Bloch equations steady-state solution to constant excitation . 60 3 Methods 63 3.1 Introduction . 63 3.2 Proton Density Imaging . 63 3.3 Relaxation Mapping . 64 3.3.1 RARE-VTR . 65 3.3.2 MSME . 67 3.4 Magnetic Field Mapping . 69 3.4.1 B0 mapping . 69 3.4.2 B1 mapping . 70 4 Rabi continuous wave spectroscopy 73 4.1 Introduction . 73 4.2 Theory . 74 4.2.1 Rabi modulated excitation . 74 4.2.2 Observed NMR signal . 75 4.2.3 Spectroscopy as an inverse problem . 76 4.3 Methods and Materials . 76 4.3.1 The response of off-resonance spins . 79 4.3.2 Rabi modulated spectroscopy . 79 4.4 Results . 83 11 12 CONTENTS 4.4.1 The response of off-resonance spins . 83 4.4.2 Rabi modulated spectroscopy . 83 4.5 Discussion . 86 4.6 Conclusion . 87 5 Rabi continuous wave imaging 89 5.1 Introduction .
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