Highly Accelerated Fmri Using Non-Cartesian Trajectories: Enhanced Data Acquisition and Enabling Real-Time Reconstruction Disser
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Highly Accelerated fMRI Using Non-Cartesian Trajectories: Enhanced Data Acquisition and Enabling Real-Time Reconstruction Dissertation zur Erlangung des Doktorgrades der Fakultät für Mathematik und Physik der Albert-Ludwigs-Universität Freiburg im Breisgau vorgelegt von Bruno Thomas Riemenschneider geboren am 17.12.1984 in Tübingen Dezember 2019 Dekan: Prof. Dr. Wolfgang Soergel Leiter der Arbeit: Prof. Dr. Dr. h.c. Jürgen Hennig Referent: Prof. Dr. Dr. h.c. Jürgen Hennig Koreferent: Prof. Dr. Oliver Waldmann Prüfer: Prof. Dr. Günter Reiter Prof. Dr. Thomas Filk Datum der mündlichen Prüfung: 06.02.2020 Contents 1 Introduction1 2 Physical Background5 2.1 Particle with Spin . .6 2.2 Ensemble of Spins in a Magnetic Field . .7 2.2.1 Density Operator . .7 2.2.2 Magnetization at Thermal Equilibrium . .7 2.2.3 Bloch Equations Without Relaxation . .9 2.2.4 Resonant Absorption of Energy - Radiofrequency Pulse . 10 2.2.5 Relaxation . 12 2.2.6 Solution of the Bloch Equations . 16 2.3 MR Signal Formation . 17 2.3.1 Faraday’s Law in Magnetization Dependence . 17 2.3.2 Induction by the Spin Ensemble . 18 3 Magnetic Resonance Imaging 19 3.1 Signal Demodulation and Signal Equation . 20 3.2 Encoding Image Information . 21 3.2.1 Fourier Imaging and k-Space . 22 3.2.2 Field Inhomogeneities and Local Macroscopic Effects . 23 3.3 k-Space Information in Unaccelerated MRI . 25 3.3.1 Fourier Transform . 25 3.3.2 Nyquist Sampling Criterion . 28 3.3.3 MRI as iDFT of truncated Fourier Series Coefficients . 28 3.4 General Image Reconstruction via Pseudoinverse . 30 3.4.1 Matrix Formulation of the Signal Equation . 31 3.4.2 Pseudoinverse Method . 32 3.4.3 Point Spread Function . 34 3.5 Measurement vs. Reconstruction Model . 35 3.6 Parallel Imaging . 36 3.7 Signal-to-Noise Ratio . 37 3.7.1 Thermal Noise Propagation . 38 3.7.2 Temporal Noise . 40 3.8 MR Imaging Sequence . 40 3.8.1 Spectral Saturation . 41 3.8.2 Volume-Selective RF Pulses . 42 3.8.3 Steady-State Magnetization . 42 3.8.4 Gradient Spoiling . 43 3.8.5 Gradient-Echo (fMRI) Sequence . 43 3.8.6 Physical Constraints . 45 3.9 Functional MRI . 46 3.9.1 Hemodynamic Response Function . 46 3.9.2 Functional Connectivity . 47 vi Contents 3.9.3 Advanced fMRI Techniques . 48 4 Own Contributions 51 5 Investigation of Off-Resonance-Gradient Vulnerability due to Variable-Density Sampling 53 5.1 Motivation . 54 5.2 Theory . 54 5.2.1 Off-Resonance . 54 5.2.2 Variable-Density Sampling . 55 5.3 Methods . 57 5.3.1 Off-resonance Model . 57 5.3.2 Trajectories . 58 5.3.3 Simulation Model and Image Reconstruction . 59 5.4 Results . 60 5.5 Discussion . 63 5.6 Conclusion . 64 6 Trading Off Spatio-Temporal Properties in 3D High-Speed fMRI Using Inter- leaved Stack-of-Spirals Trajectories 65 6.1 Motivation . 66 6.2 Material and Methods . 67 6.2.1 Trajectory Design . 67 6.2.2 Data Acquisition . 68 6.2.3 Signal Simulation and Image Reconstruction . 70 6.2.4 Time Series Processing . 70 6.2.5 Thermal Noise Propagation . 71 6.2.6 tSNR . 71 6.2.7 Functional Characterization . 71 6.3 Results . 72 6.3.1 Image Quality . 72 6.3.2 Thermal Noise Propagation . 73 6.3.3 tSNR . 76 6.3.4 Functional Characterization . 77 6.4 Discussion . 80 6.4.1 Image Quality . 80 6.4.2 SNR . 82 6.4.3 Functional Characterization . 83 6.5 Conclusion . 83 7 Targeted Partial Reconstruction for High-Speed fMRI Neurofeedback 85 7.1 Motivation . 86 7.2 Theory . 86 7.2.1 Voxel-Wise Reconstruction . 87 7.2.2 Volume-wise Reconstruction . 88 7.2.3 Efficiently Approximated Reduced-FOV Reconstruction . 91 Contents vii 7.3 Methods . 94 7.3.1 Data Acquisition . 94 7.3.2 General Reconstruction Details . 94 7.3.3 Voxel-wise Reconstruction . 95 7.3.4 Volume-wise Reconstruction . 95 7.3.5 Efficiently Approximated Reduced-FOV Reconstruction . 96 7.3.6 Feedback Scan Workflow . 97 7.4 Results . 98 7.4.1 Voxel-wise Reconstruction . 98 7.4.2 Volume-wise Reconstruction . 98 7.4.3 Efficiently Approximated Reduced-FOV Reconstruction . 102 7.4.4 Feedback Scan Implementation Performance . 103 7.5 Discussion . 105 7.5.1 Workflow and Implementation . 105 7.5.2 Reconstruction quality . 106 7.5.3 Reconstruction phase correction . 106 7.6 Conclusion . 107 8 Conclusion and Outlook 109 8.1 Conclusion . 109 8.2 Outlook . 110 A Appendix 111 A.1 Symbols and Definitions . 111 A.2 Abbreviations . 115 Journal Publications 117 Bibliography 119 Acknowledgments 131 1 Introduction While the first effects of electron and even nuclear spin were measured already in the 1880s by Michelson,1, 2 the fine and hyper fine structures visible in the spectra obtained with the Michelson Interferometer were not yet understood. The idea of quantization of subatomic particle properties was still unborn. Also the first direct experimental evidence of quantized spins of particles that was published in 1922 by Stern and Gerlach3 was still wrongly interpreted as a quantized atomic angular moment at the time. Only 3 years later, in an effort to explain the fine structure of the hydrogen spectrum, Uhlenbeck and Goudsmit4 were the first to publish the hypothesis of a "quantized electron rotation". Interestingly, various (nowadays famous) physicists had discarded the idea as unrealistic in the year before this publication.5 6 After Pauli’s formulation of the Schrödinger equation for spin-1⁄2 particles in 1927, Dirac derived the famous Dirac equation by factorizing the relativistic energy momentum equation in 1928.7 The Dirac equation is counted as one of the greatest successes of theoretical physics, being consistent with both quantum mechanics and special relativity, describing all massive spin-1⁄2 particles with the Dirac Spinors that arise along the derivation. Stern perfected the particle beam method in the years after the Stern-Gerlach experiment, and, eventually, in 1933 presented the first experimental data on deflecting a hydrogen beam8 in an inhomogeneous magnet field together with Frisch. This represented the first direct evidence of the proton spin, and moreover contradicted the gyromagnetic values predicted by Dirac at the time, leading to further discussion of the g-factors that Landé introduced already in 1921 to explain the anomalous Zeeman effect.9 A former student of Stern’s and his molecular beam method, Rabi conducted the first direct measurement of nuclear spin resonance (NMR) in 1938, manipulating the nuclear spins in a molecular beam.10 NMR experiments in solids and liquids followed by Bloch and Purcell, independently from each other, in 1946.11, 12 The first medical and physiological application of NMR to biologic tissue samples was performed by Odeblad in 1955.13 Interestingly, he had proceeded on his own after Bloch had denied a cooperation with him in 1952,14 arguing that NMR is a tool for physicists only, and not for research into physiology, medicine, or biology. Until the early 1970’s, however, all NMR measurements lacked spatial encoding of the measured samples in more than one dimension along a constant magnet field gradient. Lauterbur introduced the idea of using spatially varying magnetic field gradients to encode multiple dimensions in 1973,15 originally calculating a 2-dimensional image from multiple 2 Introduction 1-dimensional Larmor frequency projections. In the same year, Mansfield published the idea of "NMR diffraction",16 which also.