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Seeing sleep: real-time MRI methods for the evaluation of sleep apnea
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Seeing sleep: real-time MRI methods for the evaluation of sleep apnea
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SEEING SLEEP: REAL-TIME MRI METHODS FOR THE EVALUATION OF SLEEP APNEA by Ziyue Wu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BIOMEDICAL ENGINEERING) December 2015 Copyright 2015 Ziyue Wu Dedication To my mom, dad, wife and Eric. ii Acknowledgments “It takes a village to raise a child.” When looking back, I realize it certainly also takes a village to produce a PhD. This dissertation would not have been pos- sible without all the people who have given me support, help and encouragement through my ups and downs over the years. Among them, I would like to give special acknowledgements to a few. I have had the greatest fortune to work with my mentor, Prof. Krishna S. Nayak. To Krishna, it was you who introduced me to the amazing world of MRI and inspired my greatest interests.You taught me by example on how to make good presentations and how to write clear scientific papers. I appreciate your incredible inspiration, intuition and style of advising. For me, you are a lifetime friend, a role model, and the coolest advisor ever! I am deeply appreciative of being a member of the Magnetic Resonance Engi- neering Lab at USC. It has been a second family to me and I have thoroughly enjoyed my time here. To Yoon-Chul Kim, thank you for taking care of me when I just started and for acting as my second mentor; to Weiyi Chen, thank you for being my late night scan buddy in the lab; to Xin Miao, thank you for constantly asking all the questions that forced me to consolidate and deepen my MR physics knowledge; to Vanessa Landes, thank you for always showing up at 8AM and reading together with me those tedious papers; to Terrence Jao and Hung Phi Do, iii thank you for all those fruitful discussions when I got stuck; to Sajan Lingala, Yi Guo, and Yinghua Zhu, thank you for being my mathematical encyclopedia for all the recon questions; to Eamon Doyle and Ahsan Javed, thank you for bringing up those interesting topics, both inside and outside MRI, and of course, your IT support. I also thank past MREL members Harry Hu, Marc Lebel, Travis Smith, Samir Sharma, and Mahender Makhijani for helping me get started when I first joined the lab. I am also very grateful to Drs. Michael Khoo, Justin Haldar, Sally Ward, and Eric Kezirian. My research topic is interdisciplinary by nature, your broad range of expertise has provided me so many valuable insights from different aspects that I would otherwise cannot possibly think of. To Mischal Diasanta and Gloria Halfacre, thank you for taking care of all the administrative issues and making my life a lot easier. Finally, but by no small margin most importantly, I pay the highest tribute to my immediate family. To my mom and dad, I cannot appreciate enough your unreserved love and support throughout my whole life. As your only son, I am deeply indebted that I could not accompany you often ever since I went to college. To my wife Lu, thank you for all your sacrifice, so that I can focus on pursuing my academic goals; thank you for everything we have experienced together, I look forward to sharing with you the rest of our lives. To Eric, you were spending your final month inside your mom’s belly while I was writing most part of this dissertation, I hope you will enjoy it when you grow up! iv Contents Dedication ii Acknowledgments iii List of Tables vii List of Figures viii Abstract x 1 Introduction 1 2 Magnetic Resonance Imaging 4 2.1 Nuclear Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Stages in MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Accelerating MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 Non-2DFT Trajectories . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 Parallel Imaging . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.3 Multiband Excitation . . . . . . . . . . . . . . . . . . . . . . 15 2.3.4 Compressed Sensing . . . . . . . . . . . . . . . . . . . . . . 15 3 Fast Real-Time MRI for Airway Collapsibility Measurements 16 3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 19 3.1.2 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1.3 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.4 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 v 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4 Anisotropic Field-of-View Support for Golden-Angle Radial Imaging 32 4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5 Characterization of MRI Acoustic Noise and Implications for Noise Reduction 47 5.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6 Minimum Field Strength Requirements for Proton Density Weighted MRI 63 6.1 Theory & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 7 Concluding Remarks 78 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7.2 Future Work and Remarks . . . . . . . . . . . . . . . . . . . . . . . 80 Bibliography 83 A Inverse CDFs of spoke density for anisotropic FOV 94 B Signal Relaxation at Lower Field for Common Sequences 96 vi List of Tables 3.1 Compliance and P close during sleep and wakefulness . . . . . . . . . 28 3.2 Comparison of compliance and P close among different groups . . . . 29 3.3 Airway directional change . . . . . . . . . . . . . . . . . . . . . . . 29 5.1 Homogeneity & superposition test for different gradient Axes . . . . 55 5.2 Acoustic noise prediction . . . . . . . . . . . . . . . . . . . . . . . . 57 6.1 Assumptions for low field simulation . . . . . . . . . . . . . . . . . 66 vii List of Figures 2.1 Polarization of magnetic spins . . . . . . . . . . . . . . . . . . . . . 5 2.2 Excitation and precession of magnetization . . . . . . . . . . . . . . 6 2.3 Relaxation of magnetization . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Components of MR scanner . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Selective excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 GRE and SE sequences . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.7 2DFT reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.8 Common non-2DFT trajectories . . . . . . . . . . . . . . . . . . . . 14 3.1 Imaging modalities for sleep apnea . . . . . . . . . . . . . . . . . . 18 3.2 Experimental setup for airway collapsibility measurement . . . . . . 20 3.3 CAIPIRINHA RF excitation . . . . . . . . . . . . . . . . . . . . . . 22 3.4 Modified GA sampling for CAIPIRINHA . . . . . . . . . . . . . . . 23 3.5 Representative frames of open and collapsed airway . . . . . . . . . 26 3.6 Compliance and P close calculation . . . . . . . . . . . . . . . . . . . 27 4.1 Golden angle for anisotropic FOV . . . . . . . . . . . . . . . . . . . 35 4.2 PSFs of elliptical FOV sampling . . . . . . . . . . . . . . . . . . . . 38 4.3 Golden angle for anisotropic FOV . . . . . . . . . . . . . . . . . . . 39 4.4 Phantom images with different FOVs . . . . . . . . . . . . . . . . . 40 viii 4.5 In-vivo images with different FOVs . . . . . . . . . . . . . . . . . . 42 4.6 Benefit of elliptical FOV . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1 Input gradient waveforms for linearity test . . . . . . . . . . . . . . 50 5.2 Correction of time shifts . . . . . . . . . . . . . . . . . . . . . . . . 53 5.3 Homogeneity & superposition test . . . . . . . . . . . . . . . . . . . 55 5.4 Transfer functions of all gradient axes . . . . . . . . . . . . . . . . . 56 5.5 Examples of predicted acoustic noise spectrum . . . . . . . . . . . . 58 5.6 Transfer functions of different body habitus . . . . . . . . . . . . . 59 5.7 Transfer functions of different locations . . . . . . . . . . . . . . . . 60 6.1 Simulation of low-field k-space . . . . . . . . . . . . . . . . . . . . . 68 6.2 Phantom validations of simulated SNR change . . . . . . . . . . . . 75 6.3 Application to upper airway compliance measurement . . . . . . . . 76 6.4 Application to abdominal fat-water separation . . . . . . . . . . . . 77 ix Abstract M agnetic Resonance Imaging (MRI) is a non-invasive medical imag- ing technique that can visualize static anatomical structures as well as dynamic changes in arbitrary orientations. This dissertation is focused on one particular application of MRI - imaging the upper airway dynamics for the evalua- tion of sleep apnea. It targets the three biggest challenges faced by this particular application: slow acquisition speed, loud acoustic noise, and high financial cost. First, I introduce a real-time imaging method that I developed for the upper airway. It can significantly reduce acquisition time by up to 33 times than conven- tional 2DFT imaging. It combines several acceleration techniques: simultaneous multi-slice excitation, non-Cartesian (radial) sampling trajectory, parallel imag- ing, and compressed sensing reconstruction. The saved acquisition time is used for better spatial coverage, spatial and temporal resolutions that are needed for accurate airway collapsibility measurements. Important clinical findings enabled by the proposed approach are also discussed. Second, Idescribethedesignandimplementationofagolden-anglebasedradial sampling strategy that supports anisotropic FOV. The benefit of this method increases with FOV asymmetry and can reduce 33% scan time when the major- to-minor ratio is 2:1 for elliptical FOV. Phantom and in vivo cardiac experiments x have confirmed the effect of reduced streaking artifacts compared to conventional GA sampling. Next, I present the evaluation and improvement of an independent linear model for gradient-induced MRI acoustic noise. The results show that the errors are less than 3% for all physical gradient axes. A new method that synchronizes measured acoustic impulse response for the three axes have reduced prediction error from 32% to 4% when all gradients are on simultaneously. The gradient-sound transfer functions are found to be highly dependent on body habitus and location beyond 1 KHz. Implications for reducing acoustic noise based on the model are discussed. Finally, I illustrate the framework for simulating lower-field acquisitions based on data acquired at a higher field. To date, standard clinical MRI (1.5/3 T) has proven to be cost-prohibitive for many applications, including imaging sleep apnea, to benefit large-scale population. The simulation framework has demonstrated that comparable diagnostic values can be achieved at B 0 as low as 0.2 T with the methods we used for imaging sleep apnea. A classic description of the principles of MRI, as well as the summary and future remarks about this dissertation are also presented. xi Chapter 1 Introduction Magnetic resonance imaging (MRI) is a technique that uses magnetic fields to create tomographic images without exposure to ionizing radiation. When used in medicine, it can generate both anatomical and functional images with different contrast, andhasbeenusedextensivelytoexaminealmostallpartsofhumanbody. MRI is arguably the single technique that relates to the most Nobel Prizes by far. Thephenomenonofnuclearmagneticresonance(NMR),inwhichnucleiabsorband re-emitelectromagneticenergyattheirspecificresonancefrequenciesinamagnetic field, wasfirstdescribedbyI.I.Rabi[1]in1937. Itwasthenexperimentallydemon- strated by Felix Bloch [2] and Edward Purcell [3] in 1946, independently. Since then, it was used extensively to identify chemical compositions based on different atomic resonance frequencies, a technique developed by Richard Ernst in 1966 [4], also known as magnetic resonance spectroscopy (MRS). Kurt Wüthrich used MRS to determine the three-dimensional structure of biological macromolecules in 1982 [5]. In 1973, Paul Lauterbur [6] used gradient magnetic fields to resolve the objects spatially and made the very first MR image. Peter Mansfield later introduced the mathematical formalism and also developed echo-planar imaging (EPI) [7], which enabled functional MRI studies. All seven of them have won a total of four and a half Nobel Prizes in physics, chemistry, and physiology or medicine. Ever since these early developments, MRI has experienced rapid growth and has matured as a powerful medical imaging modality. It is a non-invasive tomog- raphy technique that can visualize anatomical structures with excellent soft tissue 1 contrast in arbitrary orientations. Sometimes confused with CT, MRI involves no ironizing radiation and can be safely performed in many dynamic applications, routine therapeutic monitoring or preventative screening. MRI is also capable of measuring flow, susceptibility, chemical composition and metabolic activities. By manipulating the physics behind it, there is an enormous flexibility of choosing optimal contrast, image resolution, and spatial coverage for a specific application. This dissertation is focused on one particular application of MRI - imaging upper airway dynamics for the evaluation of sleep apnea. This is essentially a fast imaging problem. Like mainstream MRI applications such as neural or cardiovas- cular imaging, the mechanisms that enabled MRI also pose a fundamental limit on imaging speed in conventional MRI. Besides higher financial cost and less patient comport, longer scan time due to the demand of high resolution and large spatial coverage often inevitably leads to motion artifacts, temporal blurring, and signal loss. Therefore how to speed up MRI without degrading diagnostic value is critical to many new applications, including the one focused here. The MR imaging process can be roughly divided into three parts: excitation phase, acquisition phase, and reconstruction phase. This dissertation describes the techniques I have applied in each of the phase and their synergistic combination to accelerate the imaging process. I will also address the other two major issues encountered in imaging sleep apnea, i.e., acoustic noise and economic cost. The outline is as follows: Chapter 2: Magnetic Resonance Imaging ThischaptercontainsthebasicoverviewofMRIprinciples. Typicalstagesofan MRIscanaredescribed. Abriefintroductionoftheaccelerationtechniquesthat havebeenappliedattheexcitationphase, acquisitionphase, andreconstruction phase is also included. 2 Chapter 3: Fast Real-Time MRI for Airway Collapsibility Measure- ments This chapter describes a comprehensive method for measuring airway collapsi- bility using MRI. This method combines simultaneous multi-slice excitation, non-Cartesian trajectory, parallel imaging, and compressed sensing. Chapter 4: Anisotropic Field-of-View Support for Golden-Angle Radial Imaging This chapter describes the design of golden-angle radial trajectory tailored for non-circular FOV support. This technique can save time for scanning objects with anisotropic shape and can be combined with 2D RF excitation. Chapter 5: Characterization of MRI Acoustic Noise and Implications for Noise Reduction This chapter describes an independent linear model for gradient acoustic noise characterization and prediction. The implications of acoustic noise reduction in routine imaging is also explored. Chapter 6: Minimum Field Strength Requirements for Proton Density Weighted MRI This chapter presents a framework for simulating low-field PDw MRI acquisi- tions based on high-field data. Low-field MR scanner is more affordable than clinical high-field scanner. This framework can be used to predict the minimum B 0 field strength requirements for MRI techniques. Chapter 7: Summary & Future Work Thischaptercontainsthesummariesandremarksofadvantagesandlimitations of the current work as well as possible future directions. 3 Chapter 2 Magnetic Resonance Imaging This chapter contains a concise description of the principles of MRI. Although fundamentally linked to quantum mechanics, the physics of MRI can be more intuitively understood and easily analyzed in a classical way, as also described in many popular textbook [8–11] in greater detail. 2.1 Nuclear Magnetic Resonance Although the word “nuclear” has been purposely skipped in MRI due toits neg- ative (but mistaken) associations of ionizing radiation, nuclear magnetic resonance is the foundation of MRI. Polarization: Atoms with an odd number of protons and/or neutrons possess anuclearangularmomentumandcanbecharacterizedasspinningchargedspheres, orsimplyspins. Theseelectricallychargedspinswillactasmagneticdipoles, whose directions are random when no external magnetic field is present. Therefore, the sumofthesemagneticdipolesperunitvolume, orthe magnetizationM, iszero. As shown in Figure 2.1. When an external magnetic field is applied, all the spins will align either parallel (n + ) or anti-parallel (n − ) to the applied field with a slightly greater number in the parallel direction. Their ratio is given by the Boltzmann distribution: n − n + =e −γ~B 0 /kT (2.1) 4 B 0 No External Magnetic Field With External Magnetic Field a) b) Figure 2.1: a) The directions of spins are random when no external magnetic field exists. b) When an external magnetic field is applied, all the spins align either parallel or anti-parallel to the applied field, with a slightly greater number in the parallel direction. This results in a net magnetization that points towards B 0 . Here γ is the gyromagnetic ratio for a certain nuclear species. When 1 H is imaged, as in most clinical applications, γ/2π = 42.6MHz/T. ~ is Planck’s con- stant, B 0 is the external magnetic field strength, k is Boltzmann’s constant, and T is absolute temperature. An equilibrium net magnetization is thus created due to the excessive parallel spins, which is commonly termed M 0 : M 0 = Nγ 2 ~ 2 I z (I z + 1)B 0 3kT (2.2) where N is the number of spins per unit volume, I z = 1/2 for 1 H. Precession: Each spin has a intrinsic resonance frequency, determined by its gyromagnetic ratio and surrounding magnetic field: ω =γB (2.3) This is known as Larmor frequency. When certain external radiofrequency (RF) pulse whose frequency matches a spin’s Larmor frequency is applied, the spin will be excited and perturbed from its equilibrium state, and will rotate about the axis 5 B 0 ω M B 0 M B 1 a) b) Figure2.2: a)AftercertainRFpulseisapplied,M isperturbedfromitsequlibrium state. Meanwhile, it also precesses about the B 0 axis at its Larmor frequency. b) The same process is usually presented in the rotating frame whose coordinates rotate about B 0 at the spins’ Larmor frequency. As a result, B 1 appears to be static and M rotates about B 1 . of alignment at its Larmor frequency (not to be confused with spin’s self rotation). This process is know as precession (Figure 2.2). The RF pulse also rotates about B 0 at the spins’ Larmor frequency and is usually noted as B 1 . Relaxation: If the B 1 pulse is retracted, the magnetization tends to go back to its equilibrium state. This process is called relaxation and can be divided into two components: longitudinal (parallel to B 0 , commonly denoted as z direction) relaxation and transverse (perpendicular to B 0 , commonly denoted as xy plane) relaxation. As also illustrated in Figure 2.3, they both follow exponential decay: M 0 −M z (t) =M 0 e −t/T 1 (2.4) M xy =M 0 e −t/T 2 (2.5) Therefore the two relaxation processes are also known as T 1 decay and T 2 decay respectively. T 2 also counts for the microscopic dephasing of the transverse com- ponent and is always shorter than T 1 . 6 M 0 a) b) M z M 0 M xy t t M 0 [1-exp(-t/T1)] M 0 exp(-t/T2) Figure 2.3: a) Longitudinal relaxation. b)Transverse relaxation. The dynamics of the magnetization described above can be combined into the Bloch equation: dM dt =M×γB− M x x +M y y T 2 + (M 0 −M z )z T 1 (2.6) where x,y,z are the unit vectors. Let B = B 0 z, the solution in matrix format becomes: M x (t) M y (t) M z (t) = −1/T 2 γB 0 0 −γB 0 −1/T 2 0 0 0 −1/T 1 R z (ω 0 t) M x (0) M y (0) M z (0) + 0 0 M 0 (1−e −t/T 1 ) (2.7) where R z (ω 0 t) is the rotation matrix describing M precessing about z-axis, M x,y,z (0) stands for the initial condition. Due to the existence of B 0 , only the transverse component can be detected. If we define M xy ,M x +iM y (2.8) 7 Figure 2.4: Left: A GE Signa HDxt 3T scanner, which was used to conduct experiments in this dissertation. Maximum gradient amplitude and slew rate are 40 mT/m and 150 mT/m/ms respectively. Right: Key components of a typical MR scanner (adapted from www.howtolearn.com). then the transverse magnetization at location r and time t can be written as M xy (r,t) =M xy (r, 0)e −iω 0 t e −t/T 2 (r) e −iΔω(r)t (2.9) Here the last exponential term is included to account for local field inhomogeneity caused by nonuniform B 0 and susceptibility. 2.2 Stages in MRI A typical clinical scanner, as shown in Figure 2.4, has three core components: a mainmagneticfieldB 0 , anoscillatingmagneticfieldB 1 , andthreepairsofgradient coils generating linear magnetic field G x ,G y ,G z in three orthogonal directions. These components are essential in order to acquire an MR image, which can be roughly segmented into four phases. 8 r B 1 (t) ω ω 0 Δr ∆ω=γGΔr FT slice profile Figure 2.5: The gradient coils create a linear gradient field on top ofB 0 across the whole object. The gradient amplitude can be tuned so that the RF’s frequency band matches the spins’ Larmor frequency range within the region of interest. Only that region satisfies resonance condition and will be excited. 2.2.1 Polarization As can be seen in Eqn 2.2,B 0 is needed to generate a net magnetization and is the only tunable parameter for human imaging. Moreover, the ratio in Eqn 2.1 is 0.999993 at 1 T and 310 K, implying only 3.5 ppm more spins in the parallel state. Therefore, a strong B 0 is required to be always on in order to make the signal detection feasible. Most clinical scanners operate at 1.5 T/3 T today (compared to the earth’s magnetic field 50 μT). 2.2.2 Excitation Spin magnetizations are too small compared to B 0 and not detectable unless they are perturbed from z-axis once the resonance condition is met. This is achieved by creating an oscillating magnetic fieldB 1 in the transverse plane, mod- ulated by the spins’ Larmor frequency. It is also known as RF pulse because its frequency usually falls within radiofrequency range. If only a small region of the whole body needs to be imaged, the linear gradient field can be turned on together with the RF pulse to achieve selective excitation. 9 The resonance frequencies of all the spins now vary linearly in the gradient direc- tion. If a band-limited RF pulse is played simultaneously, then only the spins whose Larmor frequencies fall within the range of the RF pulse’s bandwidth will be excited. As shown in Figure 2.5, one can change the gradient amplitude to tune the excited slice thickness for a particular RF pulse. The slice profile is approxi- mately the Fourier transform of the RF envelope. This is known as the small tip approximation, which is accurate for flip angles of up to 90 ◦ . Band-limited Sinc RF pulse is extensively used in MRI because it produces a near-rectangular slice profile. 2.2.3 Acquisition Right after the excitation phase, all the excited magnetizations now precess and act like RF sources. By placing an RF receiver coil perpendicular to the transverse plane, electrical signals can be produced in the coil. This signal is called free induction decay (FID): s(t) = Z V M xy (r,t)dr = Z V M xy (r, 0)e −iω 0 t e −t/T 2 (r) e −iΔω(r)t dr = Z V M xy (r, 0)e −iω 0 t e −t/T ∗ 2 (r) dr (2.10) where T ∗ 2 is also a decay constant combining the effects of T 2 decay and off- resonance intra-voxel dephasing. The object cannot be resolved spatially by FID. In order to form an image, each voxel needs to be spatially encoded. This can be achieved by applying the 10 gradient fields, which results in an accumulated linear phase across the object in arbitrary direction: s(t) = Z V M xy (r,t)e −iγ R t 0 G(τ)·rdτ dr (2.11) Consider in the simplest case a 1D static object and neglect relaxation and off- resonance. After demodulation, the signal becomes s(t) = Z x M(x)e −iγ R t 0 Gx(τ)xdτ dx = Z x M(x)e −i2πγkx(t)x dx =s(k x ) (2.12) wherek x (t) = γ 2π R t 0 G x (τ)xdτ. This is the exact format of Fourier transform (FT), implying k x is the spatial frequency spectrum of M(x). By sampling s(k x ) with constant G x turned on, M(x) can be calculated by a simple inverse FT. To form a 2D image, the same method can be applied in y direction. s(k x ,k y ) = Z x,y M(x,y)e −i2π(kx(t)x+ky (τy )y)) dxdy (2.13) Notice here k y (t) = γ 2π R τy 0 G y (τ y )ydτ, which is slightly different from k x (t). To avoid ambiguity, G y is usually turned on before each sampled readout line and different initial phases are created. Therefore, y direction here is called phase encoding (PE) direction, while x direction is called frequency encoding (FE) or readout direction. The image is thus acquired in thek x -k y spatial frequency space, commonly known as the k-space. The gradient amplitude can be thought of the speed of traversing k-space. Because signal starts to decay immediately after excitation, and there may not be enough time to sample all the desired k-space locations before it disappears, a 11 DAQ RF Gx Gy Gz GRE TE DAQ RF Gx Gy Gz SE TE 180 90 90 Figure 2.6: Typical plots of GRE and SE pulse sequences. The same sequence is repeated every TR (repetition time), except G y changes before each readout. TE (echo time) is calculated from the center of RF pulse to the formation of echo. refocused echo is often required in practical. This can be achieved by either playing a bipolar gradient, or two unipolar gradients seperated by a 180 ◦ RF refocusing pulse. They are commonly known as gradient echo (GRE) and spin echo (SE) sequences respectively, as plotted in Figure 2.6. GRE only refocuses the dephasing due to the applied gradeint itself, while SE also refocuses the dephasing caused by field inhomogeneity. Therefore, GRE signal followsT ∗ 2 decay and SE signal follows T 2 decay. 2.2.4 Reconstruction Based on Eqn 2.13, the image m(x,y), represented by its proton density dis- tribution M(x,y), can be reconstructed. If all the samples are on the Cartesian grid, a simple inverse 2D discrete Fourier transform ofs(k x ,k y ) will suffice (Figure 2.7). k-Space must be sufficiently sampled to avoid aliasing and achieve the desired resolution. FOV x = 1/Δk x ; FOV y = 1/Δk y (2.14) 12 Δk x Δk y 2k max,x =1/Δx 2k max,y =1/Δy FOV x =1/Δk x FOV y =1// Δk y 2DFT Figure 2.7: k-Space is typically sampled line by line on a Cartesian grid. if it is sufficiently sampled, the image can be reconstructed by a simple 2D discrete Fourier transform. The reconstructed image is a sagittal portrait of myself. Δx = 1/(2k max,x ); Δy = 1/(2k max,y ) (2.15) If the relaxation term is added back to Eqn 2.13, m(x,y) will also be weighted by different tissue relaxation properties. By selecting different sequences and/or tuning imaging parameters, certain contrast such as T 1 or T 2 can be enhanced in additiontoprotondensityweighting. Ifthereadouttimeisnotnegligiblecompared to T 2 , or if the off-resonance term is added back, Eqn 2.13 no longer fits a perfect Fourier transform. As a result, different artifacts will be observed, depending on different sampling strategies described below [12]. 2.3 Accelerating MRI 2.3.1 Non-2DFT Trajectories Even though 2DFT sampling is the most convenient and dominates clinical imaging, sometimes non-2DFT trajectories (Figure 2.8) are preferred. EPI and spiral trajectories acquire more samples per excitation and traverses k-space faster, 13 EPI spiral radial Figure 2.8: Common non-2DFT trajectories. but are more sensitive to T 2 decay and off-resonance. Radial trajectory is slower but is less sensitive to undersampling and more robust to flow and motion artifacts. When non-Cartesian sampling is used, a process known as gridding [13] is required before discrete FT can be applied. 2.3.2 Parallel Imaging Parallel imaging (PI) is a technique that utilizes an array of localized receiver coils. Multi-channel coils were initially developed to boost signal-to-noise ratio (SNR), but have also been used to accelerate scans by acquiring a reduced amount of k-space data. Although undersampling leads to inevitable aliasing withing each receiver channel, these localized coil elements are sensitive to different regions across the object and therefore provides an extra layer of sensitivity encoding. This extra information can be applied to resolve the aliasing caused by insufficient Fourier encoding. Most PI techniques can be divided into two categories, one operates in the image domain, such as SENSE [14]; the other operates in the k-space, represented by GRAPPA [15]. 14 2.3.3 Multiband Excitation Insteadofexcitingasingleslice, multibandRFpulsescanbeappliedtosimulta- neously excite several slices. These acquired different slices will be stacked together in the image. With proper phase modulation of each RF pulse band, their relative locations can be controlled along the phase encoding direction. This technique was originally applied in MRI using Hadamard encoding [16]. Individual slice images can be unaliased by either making FOV large enough [17] or combining with other acceleration techniques such as parallel imaging [18, 19]. 2.3.4 Compressed Sensing Compressedsensing(CS)[20]isanotherwayofreducescantimes. Itisbasedon the assumption that images are sparse in some domain and can thus be represented with fewer coefficients than the number of pixels. The sparse domain can be either the image itself such as angiography, or the image transformed to other domains like wavelet. In the case of dynamic images, the constraint may also be temporal finite differences, provided that only a small region has dramatic motion over time. In the case of upper airway imaging for example, dramatic motion occurs mostly in the airway region, while the other parts of the head and neck remain mostly still. This prior information can be incorporated into the reconstruction as a sparsity constraint, so that less sampling is required to recover the original image. 15 Chapter 3 Fast Real-Time MRI for Airway Collapsibility Measurements Sleep apnea is a common disorder characterized by repetitive pauses in breath- ing or shallow breaths during sleep. Obstructive sleep apnea (OSA) is the most common type in which the apnea is caused by a physical collapse of pharyngeal airway [21]. Despite respiratory efforts, the airway obstruction results in reduced or ceased gas exchange, followed by blood oxygen desaturation, resulting in fre- quent arousals during sleep. When untreated, OSA significantly decreases quality of life and workplace productivity, and increases the risk of traffic and workplace accidents and diseases such as heart attack, stroke, obesity and diabetes. The total economic cost of OSA is estimated to be $150 billion per year in the US, a figure much higher than the direct cost of diagnosing and treating sleep apneas ($2 - 10 billion per year) [22]. Airway collapse in OSA is typically attributed to excessive soft tissues (adenoids, tonsils, soft palate, tongue, and epiglottis) and/or increased airway collapsibility. Obesity contributes to both of these factors and has been identified as a potent risk factor highly linked to OSA [23]. The prevalence of OSA has been reported to be 4% - 9% in adults and 2% in children [24], and is likely to rise due in part to the worldwide obesity epidemic [25]. The gold standard for assessing sleep apnea is polysomnography (PSG), an overnight sleep study which records a comprehensive set of physiological signals. They include brain electrical activity (EEG), eye movement, blood oxygen satura- tion, heart rate, and respiratory effort, from which sleep disorders such as apneas 16 can be identified. Apnea-Hypopnea Index (AHI), defined as the number of apnea events per hour, is used to grade the severity of sleep apnea. Patients are typically diagnosed as having mild sleep apnea when they present an AHI of 5 - 14, mod- erate sleep apnea with an AHI of 15 - 30, and severe sleep apnea if AHI exceeds 30. However, it is well known that AHI alone does not adequately quantify the extent of the breathing disturbance [26]. AHI is based on indirect measurements and does not provide any anatomical information about the airway obstruction, nor does it provide any quantitative properties that measure tissue collapsibility. Both of these are essential to the appreciation of the pathophysiology and to tai- lor treatment to individual patients. Therefore direct access of such information with an imaging tool is highly desired and attempts have been made using sev- eral modalities including fluoroscopy [27, 28], fiberoptic nasoendoscopy [29–31], cephalometry [32, 33], CT [34–36], acoustic reflection [37, 38], and more recently optical coherence tomography (OCT) [39] and MRI. Representative images from different imaging modalities are shown in Figure 3.1. MRI is a promising technique because it can provide complete 3D information, is non-invasive and involves no ionizing radiation, and is compatible with natural sleep. 3D static MRI can generate excellent tissue contrast and identify potential anatomicalriskfactorsandairwaynarrowing[40,41]. Enlargedairwaytissuessuch as the adenoids and tonsils can be easily identified with T 2 contrast and positive correlations have been found between OSA and these enlarged tissues. Tongue and neck fat are also risk factors that can be quantified using static MRI. CINE techniques have also been implemented to measure the changes of upper airway during tidal breathing [42–46]. Due to the acquisition speed constraints, data from multiple respiratory cycles are used to form one cycle of dynamic images based on respiratory gating in these methods. 17 Figure 3.1: Representative images of different modalities for the evaluation of sleep apnea. Top row left to right: fluoroscopy, fiberoptic endoscopy, CT; Bottom row: acoustic reflection, OCT, MRI. Airway compliance has been proposed as a metric for airway collapsibility [47– 49], and is defined as the change in airway cross-sectional area per unit of pressure [29]. Compliance testing involves the generation of negative pressure via brief inspiratory load (one to three breaths) during real-time imaging of a 2D axial slice. Under these conditions, airway motion can be rapid, requiring roughly 100 ms temporal and 1 mm spatial resolution [50]. The spatiotemporal resolution (1.95 mm, 667 ms) and single slice coverage [51] of conventional RT-MRI are inadequate. Alternative imaging schemes have been proposed, including 2D spiral (2.6 mm, 181 ms) [45] and EPI (1.56 mm, 160 ms) [52], interleaved multi-slice (1.6 mm/2000 ms/3-slice) [53], and 3D real-time imaging using compressed sensing (2 mm, 388 ms)[54], however, noneoftheseapproacheshaveprovidedadequatespatiotemporal resolution and coverage for airway compliance testing. Simultaneous-multi-slice 18 (SMS) or 3D imaging that covers more of the relevant pharyngeal airway (i.e. from soft palate to epiglottis) would be a major advance as it would allow more comprehensive evaluation of possible collapsing sites along the pharyngeal airway. In this work, we develop and evaluate a real-time imaging method that syn- ergistically combines several acceleration techniques – SMS, golden angle radial sampling, parallel imaging, and compressed sensing – for airway compliance mea- surement. Enabled by this method, we demonstrate, for the first time with imag- ing, that the narrowest airway site at baseline is not always the most collapsible site. Our preliminary results also suggest that both compliance and projected clos- ing pressureP close by MRI may be used to assess OSA, and that a 30 minute awake scan may be sufficient. 3.1 Methods 3.1.1 Experimental Setup Experiments were performed on a 3T GE Signa HDxt scanner (GE Healthcare, Waukesha, WI) with gradients capable of 40 mT/m amplitude and 150 T/m/s slew rate. A body transmission coil and a 6-channel carotid receiver coil (NeoCoil, Pewaukee, WI) were used. During the scan, a facemask (Hans Rudolph Inc., Kansas City, MO) that cov- ers both nose and mouth was used for measurement of airway pressure and for creating an inspiratory load for compliance testing. Small-bore tubing from the mask port was connected to an MP-45 pressure transducer (Validyne Engineering Inc., Northridge, CA) for measurement of mask pressure. The inspiratory port of the mask was connected through an extension hose to an inflatable balloon valve (Model9325, HansRudolphInc., Shawnee, KS)thatwasusedtocontroltheflowof 19 Figure 3.2: Experimental setup for airway collapsibility measurement. Left: A facemask covering nose and mouth is connected to an external hose, which con- tains an inflatable balloon. Once expanded, the balloon can block the air flow and serve as external inspiratory load. Physiological signals including facemask pressure, chest and abdomen displacements, oxygen saturation, and heart rate are simultaneously recorded and synchronized with MRI acquisition. Right: Posi- tioning of the 6-channel receiver coil. Note that subjects in this study wore all equipment shown in both panels. air entering the mask. The scan operator was able to initiate an inspiratory occlu- sion by pneumatically activating the balloon valve through an automated valve controller (Model 9330, Hans Rudolph Inc., Shawnee, KS), located in the MRI console room. The occlusion [52] served as external inspiratory load that could lead to substantial narrowing of the upper airway during inspiration. In addition, several other physiological signals were monitored and recorded during the MRI scan to determine sleep/wakefulness, as shown in Figure 3.2. An optical fingertip plethysmograph (Biopac Inc., Goleta, CA) was used to measure heart rate and oxygen saturation. A respiratory transducer (Biopac Inc., Goleta, CA) and the scanner’s built-in respiratory bellows were used to measure respiratory effort at the lower chest and abdomen. 20 Five adolescent OSA patients (3M2F, age 13-17), three adult OSA volunteers (3M, age 30-40), and four healthy adult volunteers (2M2F, age 23-30) were studied. The experiment protocol was approved by our Institutional Review Board, and informed consent was obtained from all subjects. Each recruited adolescent first underwent an overnight polysomnography which determined the severity of OSA in each subject. All adult OSA volunteers were previously diagnosed to have OSA and were using continuous positive airway pressure (CPAP) treatment at the time of studies. All healthy volunteers reported that they had no sleep disorders and no excessive daytime sleepiness. The total time inside the scanner was 1 hour for each adolescent OSA patient. All the adult OSA and healthy volunteers were inside the scanner for 30 minutes and stayed awake. 3.1.2 Data Acquisition Four axial slices were simultaneously excited based on the CAIPIRINHA tech- nique [19]. To image N slices, N unique multi-band RF pulses are applied alter- natively, as shown in Figure 3.3. The k th pulse is designed such that the phase difference between signal from adjacent slices is 2πk/N, k∈ [0,N− 1]. This cre- ates a unique linear phase along the slice selection direction. If Cartesian readouts were used this would result in a shift of individual slice images along the phase encode direction. When combined with radial sampling, it leads to destructive interference for all slices with non-constant initial RF phases, which significantly reduces the total amount of inter-slice interference [55]. Each slice can be recovered by multiplying the acquired data with the conjugate of the excited phase for the specific slice. To maximize signal destruction from other slices, it is desirable to have a uni- form distributions of spokes excited by each RF pattern. Golden Angle (GA) view 21 RF1à RF2à à à à à RF3 RF4 à à RF1 RF2 RF3 RF4 Readout #1 Readout #2 Readout #3 Readout #4 Readout #5 Readout #6 ... S1 Signals: Readout #7 Readout #8 ... RF1 RF2 0° 0° 180° 0° S1 S2 S3 0° 90° RF3 S4 0° 270° 0° 0° 180° 180° RF4 180° 0° 270° 90° S2 S3 S4 Excited slices: Figure 3.3: Illustration of 4-slice SMS excitation for CAIPIRINHA. In general, for N slices, N unique multi-band RF pulses are applied alternatively. The k th pulse generates a transverse phase difference between adjacent slices of 2πk/N, k∈ [0,N−1]. Whencombinedwithradialsampling, thisleadstosignaldestructive interference for all slices with non-compensated RF phase (via conjugate phase reconstruction). ordering [56] is known to produce almost uniform distribution forall spokes in an arbitrary temporal window. Here we adopted a modified GA radial trajectory view ordering, where the azimuthal angle increment is 111.25 ◦ /N for N-slice imaging. While still allowing retrospective temporal window size selection, this produces a more uniform distribution for spokes excited by each RF pattern compared to conventional GA. Figure 3.4 shows a representative frame of both conventional GA and modified GA sampling for 4-slice imaging. AcustomizedradialGREsequencewasusedtoscanallpatientsandvolunteers. Imaging parameters were: 5 ◦ flip angle, 200 samples per readout, FOV 200× 200 22 conventional GA 1/4 GA Figure 3.4: Modified GA sampling. One representative temporal frame with 32 spokes, for (left) conventional GA and (right) modified GA sampling trajectories for 4-slice CAIPIRINHA excitation. Spoke colors correspond to their excitation RF pulses in Figure 3.3. The modified method provides a more uniform distribu- tion of spokes excited by each RF pattern. After gridding, this leads to better cancellation of signals from slices other than the one to be preserved, especially at the more densely sampled k-space center. mm 2 , TR 4 ms. A fixed slice thickness/gap (7 mm/3 mm) were used, which led to 3- or 4-slice coverage from soft palate to epiglottis depending on the subject’s pharyngeal airway length. 3.1.3 Reconstruction Depending on the respiratory rate of each subject during the occlusion, 24- 32 spokes were used to reconstruct one temporal frame, which led to 96-128 ms temporal resolution. Non-Cartesian SENSE [57] and compressed sensing [20] with temporal finite difference as sparsity constraint [58] were used to reconstruct each slice separately by iteratively minimizing the cost function f i =||P i ES i m i −P i k|| 2 2 +λ i ||Φm i || 1 , i∈ [1,N] (3.1) 23 where i is the slice index, P i is the conjugate of the RF phase cycling pattern for slicei, E is Gridding operator, S i is coil sensitivity map, k is the acquired k-space data, Φ is the finite temporal difference, andm i is the individual slice image to be solved. The regularization factors λ i were chose empirically. 3.1.4 Post-processing The airway was segmented in each frame using a semi-automated region- growing algorithm [51]. For each subject, the airway area was normalized by the maximum cross-sectional area among all slices during tidal breathing to facil- itate inter-subject comparison. For each slice, data from the first two consecutive breaths within one occlusion were used. Each breath was further divided into the inhale portion and exhale potion and a linear regression (airway area vs pressure) was performed for each portion, from which the compliance (line slope) and the linearly projected closing pressureP close (horizontal zero-crossing) were calculated. Compliance andP close were averaged over two occlusions at each slice for each sub- ject. Each occlusion lasted two consecutive breaths before releasing. All slices were then divided into retropalatal and retroglossal regions and their compliance and P close values were averaged within the subject category (adolescent OSA, adult OSA, and adult control). To remove the impact of muscle tone change among different subjects as much as possible, only the calculated compliance and P close from the inhale portion of the first occluded breath were used for inter-subject average and inter-category comparison. The ratio of the maximal airway change in the left-right direction and anterior-posterior direction were also calculated for all slices in the retropalatal and retroglossal regions respectively and averaged over all subjects within different categories. 24 3.2 Results Figures 3.5 and 3.6 contain representative results from one adolescent OSA patientduringsleepusing4-sliceacquisition. InFigure3.5, thelocationofacquired slices are shown in the sagittal view. The top row on the right shows one frame at these locations when the airway is open during tidal breathing. The bottom row shows another frame when the airways are partially collapsed during one occluded breath. Figure 3.6a shows the cross-sectional area of each slice together with the synchronized mask pressure during the occluded breath. Data from the inhale potion (shaded area) was used to perform a linear regression for each slice, from which the compliance and P close values were calculated (Figure 3.6b). The R 2 values were 0.94, 0.95, 0.94, 0.91 for slice 1-4 respectively. Note that although slice 1 (red) was not the narrowest during steady state (pressure = 0 cm H 2 O), it was the most collapsible site based on compliance andP close . In contrast, slice 4 (black) had the narrowest airway area during steady state, but was the least collapsible site. We have observed this mismatch between the narrowest and most collapsible site in five out of twelve subjects so far. Table 3.1 compares the calculated compliance and P close values among the inhale/exhale portions of the first two occluded breaths during sleep and wakeful- ness, all from adolescent OSA patients. Note that while the compliance and P close changes are insignificant during sleep among different breaths and inhale/exhale portions for the same airway region, the differences are much larger during wake- fulness. Table 3.2 compares the compliance and P close values among the three subject groups during wakefulness. To minimize the impact of muscle tone change, com- pliance and P close values from the inhale portion of the first occluded breath only were listed. There is a significant difference of compliance and P close between the 25 Figure 3.5: Representative frames from one sleep apnea patient. 4-slice SMS acqui- sition covering from soft palate to epiglottis were used, as shown in the sagittal view. Top row: one frame when the airways are open during tidal breathing. Bot- tom row: one frame when the airways are partially collapsed. There is a 42% - 79% airway cross sectional area change due to the inspirational load at different loca- tions. Note that residual streaking artifacts (black arrows) can be observed due to heavy undersampling, however, they have negligible impact on airway boundary depiction. OSA (adolescent and adult) patients and healthy adult controls. Also note that adolescent OSA patients have a noticeably higher compliance and P close in the retropalatal region compared to the retroglossal region. This regional variation is insignificant in both adult OSA and control groups. Table 3.3 shows the ratio of the maximal airway change in the left-right direc- tion and anterior-posterior direction in the retropalatal and retroglossal regions for the adolescent OSA, adult OSA, and adult control groups respectively. It indicates that within the adolescent OSA group, the airways tend to be more collapsible in the RL direction than AP direction in the retropalatal region. The difference is smaller in the retroglossal region. The same trend can also be found in adult OSA group but is less obvious. The directional variance is more uniform in the adult control group. 26 a) b) Figure 3.6: Compliance and projected closing pressure (P close ) calculation. a) Cross-sectional area of the patent airway in each slice and the facemask pressure during one representative occluded breath. b) Linear regression of data from the inhale portion (shaded area in a), from which the compliance (slope) andP close (x- intercept) values are calculated. Colors correspond to the slice locations in Figure 3.5. Note that slice 4 is the narrowest at baseline, whereas slice 1 is the most compliant and has the highest P close , suggesting that it is the more likely point of collapse. 3.3 Discussion We show that SMS RT-MRI can provide valuable information to help diagnos- ing sleep apnea in addition to polysomnography. The proposed method is able to provide the desired spatiotemporal resolution and spatial coverage for the eval- uation of upper airway collapsibility. This is a preliminary study with a limited sample size and the implications discussed below require confirmation from further studies. However, we report several interesting findings. 27 Sleep Wakefulness Retropalatal Mean±SD Retroglossal Mean±SD Retropalatal Mean±SD Retroglossal Mean±SD compliance P close compliance P close compliance P close cmpliance P close B1 .095 -9.06 .085 -11.18 .087 -10.13 .077 -13.25 inhale ±.024 ±2.27 ±.015 ±2.03 ±.021 ±2.54 ±.019 ±2.91 B1 .098 -9.21 .084 -11.42 .106 -8.81 .080 -11.42 exhale ±.014 ±1.95 ±.020 ±2.53 ±.016 ±1.74 ±.013 ±1.85 B2 .103 -8.57 .090 -10.74 .081 -11.24 .068 -14.35 inhale ±.019 ±1.73 ±.017 ±2.21 ±.027 ±2.88 ±.015 ±2.16 B2 .101 -8.69 .088 -10.99 .092 -9.98 .075 -12.73 exhale ±.022 ±1.50 ±.013 ±2.27 ±.029 ±3.07 ±.017 ±2.77 Table 3.1: Compliance and P close during sleep and wakefulness. The listed mean±SD were calculated from the adolescent OSA group. Number of subjects: sleep (N = 3); awake (N=5). Two separate measurements of each slice from each subject were used. Data from the first two consecutive breaths within one occlu- sion were shown in different rows. Each breath was further divided into the inhale portion and exhale potion. Note that while the compliance and P close changes are insignificant during sleep among different breaths and inhale/exhale portions for the same airway region, the fluctuations are much larger during wakefulness, implying involuntary muscle tone change. From Figure 3.5 we can see that the proposed reconstruction is able to recover all of the relevant UA boundary information. Minor residual streaking artifacts persists but does not affect airway segmentation. This may be mitigated by sacri- ficingtemporalresolution. However, wepurposelychoseahightemporalresolution (128 ms) because it is critical to fully resolve the airway dynamics. Both the com- pliance and P close values vary among different slices, which confirms the value of simultaneous multi-slice imaging. For the number of slices, we found 7 mm slice thickness/3 mm gap, which results in 3-4 slice coverage of the pharyngeal airway, is a good balance point of spatial coverage and image quality. One important finding is that a narrower airway site during tidal breathing does not necessarily have higher compliance or P close , and therefore is not always the most collapsible (S4). Vice versa, the most collapsible airway site is not neces- sarily the narrowest during tidal breathing (S1). We observed this phenomenon in 28 Number of Retropalatal Retroglossal subjects compliance P close compliance P close Adolescent OSA 5 .087 ±.021 -10.13 ±2.54 .077 ±.019 -13.25 ±2.91 Adult OSA 3 .072 ±.018 -13.23 ±3.77 .070 ±.016 -14.31 ±3.33 Adult control 4 .042 ±.012 -24.18 ±5.14 .039 ±.008 -25.94 ±5.45 Table 3.2: Comparison of compliance and P close among different groups. Two sep- arate measurements of each slice from each subject were used. Note the significant difference of both compliance and Pclose between OSA and control. Number of Subjects Retropalatal Retroglossal Adolescent OSA 5 1.42±0.27 1.12±0.15 Adult OSA 3 1.18±0.35 0.93±0.23 Adult control 4 1.13±0.18 1.05±0.07 Table 3.3: Ratio of the maximal airway change in the left-right direction and anterior-posterior direction. The ratio is a reflection of the uniformity of airway collapse. A ratio higher than 1 indicates the airway collapses more easily in the RL direction than AP direction. approximately half of the subjects studied (2/5 adolescent OSA, 1/3 adult OSA, 2/4 adult healthy control). To the best of our knowledge, this is the first time that this finding has been verified experimentally. Currently, for OSA patients who can- nottolerateCPAPtreatmentandseeksleepsurgeries,thesuccessrateisonlyabout 60% in the short term (3 - 6 months) and can degrade to < 50% in the long term [59]. Some patients even have worse apnea after the surgeries. In these surgeries, excessive airway tissues are typically removed at the narrowest site without con- sidering their collapsibility. Although drug-induced sleep endoscopy [31] has been used clinically to identify airway obstruction site, it requires anesthesia, which may not reflect the true tissue collapsibility. We hypothesize that our finding could be the reason why sleep surgeries have low success rate. The ability of the proposed 29 method to identify the most collapsible site may help sleep surgeons identify the optimal location for intervention and potentially improve surgery success rate. From Table 3.1 we can see that the compliance and P close values have much smaller fluctuations among different occluded breaths and the inhale/exhale por- tions within one breath during sleep, when compared to wakefulness. This is likely due to the involuntary airway muscle tone change. Although ideally the airway collapsibility should be measured during sleep, it may not be feasible in practice. First, our experiment has several constraints such as supine position, wearing face- mask, and acoustic noise that may be uncomfortable to certain people. Second, MRI scan time is expensive and but falling asleep takes time and can be very unpredictable. In this study, 3 out of 5 adolescent OSA patients fell asleep within 1 hour. Therefore, it may be more practical to perform the compliance test during wakefulness, which typically requires about 20 minutes total scan room time. To minimizethemuscletonechange, whichcanbeverysubjectdependent, wepropose to use only the inhale portion of the first occluded breath for inter-subject com- parison. Under such conditions, it can still reflect the relative differences between the retropalatal and retroglossal regions. Although one should note that both compliance and P close values are smaller than during sleep. ThedifferenceofcomplianceandP close valuesbetweentheOSA(adolescentand adult) patients and healthy adult controls was significant (Table 3.2). This implies thatbothcollapsibilitymeasurescan potentially serveasbiomarkersfor diagnosing OSA. Another interesting finding is that only in the adolescent OSA group, we can see a noticeably higher compliance and P close in the retropalatal region compared to the retroglossal region. This is consistent with [60], in which the retropalatal region is also recommended for initial treatment consideration for adolescent based 30 on a large population study. This regional variation is not observed in both adult OSA and control groups. Table 3.3 indicates that within the adolescent OSA group, the airways tend to be more collapsible in the RL direction than AP direction in the retropalatal region only. This is likely due to the enlarged tonsils commonly found in OSA patients. A less obvious difference can be observed in the adult OSA group. One reason could be the adapted tissue collapsibility over the time for adults to reduce apnea. 3.4 Conclusion We have demonstrated a novel imaging method for airway collapsibility mea- surement that utilizes an inspiratory load and SMS RT-MRI. It combines several acceleration techniques including SMS, parallel imaging, modified GA radial tra- jectory, and compressed sensing, to achieve 33.3x acceleration compared to fully sampled Cartesian scanning. We have also experimentally verified that a narrower airway site does not always correspond to higher collapsibility. This finding has the potential to impact sleep surgery planning. Our preliminary results suggest that both compliance andP close , as measured by SMS RT-MRI, may serve as biomark- ers to diagnose OSA, and can be calculated with a relatively short 30 minute awake scan. 31 Chapter 4 Anisotropic Field-of-View Support for Golden-Angle Radial Imaging Radialsamplingtechniqueshavebeenusedextensivelyinmedicalimagingsince the invention of computed tomography (CT) [61]. It was also used in the first MRI experiment [6] and remains popular in the MRI community. Radial MRI supports ultra-short echo times [62] and is known to be robust to flow [63] and motion [64]. It also provides a diffuse aliasing pattern [64] and therefore less sensitive to undersampling. Although Cartesian sampling dominates most clinical MRI today, radial trajectories are still preferred in many applications, including dynamic imaging, due to these favorable properties. Standard implementations of radial imaging do not support anisotropic FOV, which leads to sampling redundancy and unnecessary scan time when the object being imaged has anisotropic in-plane dimensions (abdomen, spine, etc.). This problem was addressed by Larson et al., who proposed a method of designing fully sampledradialtrajectorieswithvariablespokedensitiesmatchedtotheanisotropic FOV [65]. However, this method alone cannot be applied with golden angle (GA) view ordering, which was first applied in MRI by Winkelmann et al. [56], and has become an important acquisition scheme for dynamic imaging applications. GA sampling has the important feature of nearly uniform radial spoke distribution for any arbitrary temporal window. The temporal window size can therefore be retrospectively selected. Prior knowledge of the expected motion dynamics and requisite temporal resolution has become less critical. 32 Since radial MRI is particularly useful in dynamic applications, the work of this paper is to extend Larson’s method and provide anisotropic FOV support for GA radial imaging. The conventional GA sampling is modified to follow the desired spoke density for any predetermined FOV shape instead of a uniform distribution, which provides a circular FOV. We used elliptical FOVs for demonstration; how- ever, the approach is compatible with any arbitrary convex FOV. This work can also be combined with 2D excitation to reduce scan times for 3D upper airway imaging, as described in the future work chapter. 4.1 Theory In radial MRI, when a convex FOV is desired, it can be expressed as a function of the azimuthal angle FOV (θ). Since the density of spokes f(θ)∝ 1/Δθ(θ)≈ k max (θ)FOV (θ +π/2) [65], an efficient GA sampling scheme should maintainf(θ) in physical k-space corresponding to the given FOV shape, for any arbitrary tem- poral window. Heref(θ) is in general not constant, and can be determined by the FOV shape. Now consider an angle-normalized space where the angles θ 0 ∈ [0, 1). In this space, the angle of the i th spoke θ 0 [i] is sampled by the conventional GA scheme: θ 0 [i] =mod[2i/(1 + √ 5, 1],i = 1, 2, 3... (4.1) This leads to an approximately uniform distribution of the spokes in the θ 0 space, i.e. f(θ 0 )≈ 1, and therefore nearly isotropic FOV for arbitrary temporal windows. The problem now becomes to find a parametric mapping θ[i] =T{θ 0 [i]} such that f(T{θ 0 }) = f(θ). T{θ 0 [i]} can then be used to transform θ 0 back to the physical k-space to get the angle in real acquisition θ[i]. Based on the inverse transform 33 sampling[66]: ifθ 0 isuniformlydistributedon [0, 1),thenθ =F −1 (θ 0 )followsdistri- butionF, whereF is the cumulative distribution function ofθ. Therefore,T{θ 0 [i]} is exactly the inverse cumulative distribution function: T{θ 0 [i]} =F −1 (θ 0 [i]). T{·} is in general difficult to calculate analytically (see Appendix A), and may be solved numerically by approximating F −1 (θ 0 ) with a function easier to compute. 4.2 Methods Without loss of generality, we consider an elliptical FOV with isotropic spatial resolution as an example. Since F −1 (θ 0 ) is very complex for elliptical FOVs, a practicalinterpolationapproachisusedherewithoutexplicitlycalculatingF −1 (θ 0 ). This interpolation approach can also be extended to any convex FOV shape. As illustrated in Figure 4.1a, first, the fully sampled radial trajectory was computed for the desired elliptical FOV using the Larson method, based on Δθ full [n] = 1 k max FOV (θ full [n] +π/2) (4.2) where the angles of the spokes are noted as θ full [n],n = [0, 1,...,N), and Δθ full [n] aretheangleincrements. N isthetotalnumberofspokes. Furtherfineadjustments were performed to improve trajectory symmetry, as described in detail in [65]. Second, the index for the i th GA spoke in the physical k-space was normalized to have the same range as the fully sampled spokes, by multiplying θ 0 by N: ind ga [i] =N∗mod[2i/(1 + √ 5), 1] =N∗θ 0 [i],i = [0, 1,...,∞) (4.3) Next, the fully sampled trajectory calculated previously, as described byθ full (yel- low dots in Figure 4.1b), can be used to generate a continuous mapping function 34 ... ind [i] = N*mod[2i/(1+√5),1] ga ind [0] = 0 ind [1] = 0.618N ga ga ind [2] = 0.236N ga ind ga θ full 0 1 2 ... N-1 = N*θ’[i] 0 0.5 1 1.5 2 2.5 3 ... 05 10 N index ind [1] ind [1] ga ga ind [2] ind [2] ga ga ind [3] ind [3] ga ga θ[1] θ[1] θ[2] θ[2] θ[3] θ[3] interpolation + parametric mapping interpolation + parametric mapping a) a) b) b) 0 0.2 0.4 0.6 0.8 1 θ’ θ Figure 4.1: Generation of golden angle radial trajectory for anisotropic FOV. a). A fullysampledradialtrajectory, indexedby[0,N), isfirstdeterminedforthedesired FOV.Theindexofthei th GAspokeind ga [i]isalsocalculated. b)Thefullysampled trajectory from a) can be described by θ full (yellow dots) and used to generate a continuousmappingfunctionbetweentheindexandθ byanyinterpolationmethod. Piecewise linear interpolation is used here (blue curve). θ[i] can be determined based on the curve. This approach is equivalent to finding T{θ} by finding an approximation ofF −1 (θ 0 ) that is easier to compute. In the case of piecewise linear interpolation, it is the same as generating a piecewise linear approximation of F −1 (θ 0 ). The range ofθ 0 is [0, 1), which corresponds to the index range [0,N). The numerically computed optimal F −1 (θ 0 ) is also plotted (red curve) for comparison. A small FOV (X:Y = 25:5 pixels, resulting in N = 15) is purposely chosen in the figure for better visualization. between the index [0,N) andθ by any interpolation method. In the simplest form of linear interpolation (blue curve), θ[i] for the i th GA spoke is computed by θ[i] =θ full [A[i]] +D[i]∗ Δθ full [A[i]] (4.4) where A[i], D[i] are the integer and decimal part of ind ga respectively, i.e., A[i] = [ind ga [i]],D[i] =ind ga [i]−A[i]. 35 This practical interpolation approach is in fact equivalent to finding T{θ 0 } by finding an approximation of F −1 (θ 0 ) that is easier to compute. In the case of piecewise linear interpolation (Figure 4.1b), it is the same as generating a piecewise linearapproximationofF −1 (θ 0 )(bluecurve),basedonwhichθ[i]canbedetermined from its corresponding θ 0 [i]. The numerically computed optimal F −1 (θ 0 ) is also plotted (red curve) for comparison. One elliptical FOV (major : minor axis = 100:20 pixels) was generated using the approach above and used as an example to perform further analysis. The point-spread-functions (PSF) of the proposed sampling schemes were generated to analyze the main lobe and side lobes inside the desired FOV. The normalized spokedensityhistogramsfordifferenttemporalwindowlengthsandacrossdifferent temporal windows were also compared to the optimal density distribution f(θ). The proposed sampling scheme was implemented on a 3T Signa HDxt scan- ner (GE Heathcare, Milwaukee, WI). Phantom images were acquired and com- pared against conventional GA sampling as well as the Larson’s method. It was also implemented on a 1.5T Avanto scanner (Siemens Medical Solutions, Malvern, PA). In vivo long-axis cardiac images were acquired using a real-time radial GRE sequence in one volunteer. The proposed method with elliptical and rectangular FOV with major-to-minor-axis ratio 1:0.4 was compared with conventional GA sampling. The sampling pattern generation and the reconstruction were also implemented in MATLAB (Mathworks, Natick, MA). All images were reconstructed using the gridding algorithm [67], with sampling density compensation factor calculated by the Voronoi approach [68]. ToquantifythebenefitofellipticalFOVimaging, thenumberofspokesrequired were compared between the fully sampled circular FOV trajectories and elliptical 36 FOV trajectories with different major-to-minor-axis ratios. This comparison was also used for the same undersampling factor in both cases. 4.3 Results Figure 4.2 & 4.3 contain representative results for an elliptical FOV (major : minor axis = 100:20 pixels). Figure 4.2a contains the PSF of the fully sampled radial trajectory using the Larson method (60 spokes). Figure 4.2b-d contain the PSFs using the proposed GA trajectories. Three consecutive temporal frames with spokes equal to the next Fibonacci number (N ga = 89) are shown. One temporal frame of conventional GA sampling with 89 spokes is also shown in Figure 4.2e. The desired FOV is plotted on top (white dash lines). Figure 4.2f-g plot the major and minor axes of the PSFs between the arrows, with colors that correspond to b-e, respectively. The fully sampled plots in a) are also shown for comparison (red dash lines). Shaded areas represent the desired FOVs. While small residual side lobes still exist inside the desired FOV using the proposed method, they are at least∼100x smaller when the spoke number is increased to the next Fibonacci number. Also note these side lobes are incoherent at different temporal frames. Conventional GA sampling produces significantly larger side lobes along the major axis. Figure 4.3 compares the sampling patterns using the proposed method with dif- ferent spoke numbers. Both Fibonacci{34, 55, 89} and non-Fibonacci{24, 40, 70} numbers are shown. The FOV ratio is identical to what is used in Figure 4.2. The corresponding normalized spoke density histogram is averaged over 100 frames. 37 a) b) c) d) short axis (N = 89) long axis (N = 89) pixel pixel 10 10 10 10 10 -4 -3 -2 -1 0 10 10 10 10 10 -4 -3 -2 -1 0 -20 20 60 100 -100 -60 -10 10 30 50 -50 -30 f) f) g) g) normalized intensity N = 60 N = 89 ga ga ga e) N = 89 ga Figure 4.2: PSFs of for an elliptical FOV (X:Y = 100:20 pixels). a) fully sampled radial sampling using the Larson method (N = 60). White dash line represents the desiredFOV.b)-d)3consecutivetemporalframesusingthemodifiedGAsampling, withspokeperframeequaltothenextFibonaccinumber89. e)onetemporalframe using conventional GA sampling, also with 89 spokes. f)-g) plots of the major and minor axes of the PSFs between the arrows, with colors corresponding to b)-e) respectively. The fully sampled plots in a) are also shown for comparison (red dash lines). Shaded areas represent the desired FOVs. Error bars represent plus or minus one standard deviations within each bin. The red line represents the optimal spoke density distribution for this FOV, i.e.: f(θ) = s cos 2 θ b 2 + sin 2 θ a 2 −1 / Z π 0 s cos 2 θ b 2 + sin 2 θ a 2 −1 dθ (4.5) where a and b are the major and minor axes of the elliptical FOV in pixel units (100, 20 in this example). The normalized density histograms indicate that the spokedistributionsareverystablefordifferenttemporalwindowlength, andacross different temporal frames. They always follow the optimal densities f(θ). 38 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 180 180 180 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 180 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 180 0 50 100 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 8 0.9 180 N =55 N =70 N =89 ga ga ga N =24 N =34 N =40 ga ga ga Figure 4.3: Sampling patterns using the proposed method. The same elliptical FOV ratio (100:20) in Figure 4.2 is used. One temporal frame is shown for each temporal width (number of spokes). The corresponding normalized spoke den- sity histogram is averaged over 100 frames and listed below. Error bars for each bin represent plus or minus one standard deviation. The optimal spoke density distribution is also plotted (red line). Figure 4.4 contains images of a ball phantom and an ultra-fine resolution phan- tom placed side by side and acquired using different methods for comparison. All images have 400×120 pixels with 0.75 mm isotropic resolution. Figure 4.4a,c were acquired using conventional GA, Figure 4.4b,d were acquired with the proposed GA for elliptical FOV, Figure 4.4e was acquired with Larson’s method satisfying 39 b) b) a) a) d) d) c) c) f) f) e) e) Figure 4.4: Comparison of phantom images with different FOVs. All images have 0.75 mm isotropic resolution, 400 x 120 pixels. a) & c) Conventional GA sampling, b) & d) proposed GA sampling for elliptical FOV. a)-b) both use 144 spokes; c)- d) both use 315 spokes. Note the significantly reduced streaking artifacts in b) & d). e) Larson’s method satisfying Nyquist rate (315 spokes). f) Proposed GA sampling satisfying Nyquist rate (377 spokes), the image quality is comparable to e). The unaliased FOV shapes are also shown (white dashed lines) for each sampling scheme. One region (white rectangle) is enlarged in the bottom row to better illustrate streaking artifacts due to undersampling. Nyquist rate. The number of spokes used in Figure 4.4a-e were 144, 144, 315, 315, and 315 respectively. The proposed GA sampling satisfying the Nyquist rate (N = 377) is also listed in Figure 4.4f. The unaliased FOV shapes are plotted in white dashed lines for each sampling scheme. The enlarged regions within the white rectangle are also shown to better illustrate streaking artifacts. The strong streaking artifacts that exist in Figure 4.4a,c are significantly reduced with the proposed sampling in Figure 4.4b,d without increasing the number of samples. When Nyquist sampling rate is met, the streaking artifacts are further reduced inside the FOV (Figure 4.4f) and the image quality is comparable to the Larson’s method (Figure 4.4e). 40 Figure 4.5 compares long-axis-view cardiac images with different sampling schemes. The top row shows one diastolic frame with 34 spokes reconstructed with gridding using conventional GA, proposed GA with rectangular and elliptical FOV (major-to-minor-axis ratio 1:0.4) sampling respectively. The unaliased FOV shapes are plotted in white dashed lines for each sampling scheme. The enlarged region of interest, together with another systolic frame are shown. The bottom rows show two frames from the same acquisition reconstructed with 55 spokes. Excess streaking artifacts can be observed in all conventional GA cases (white arrows). Figure 4.6 plots the percentage of data needed for the elliptical FOV when compared to the circular FOV radial sampling with the same acceleration factor, as a function of the major-to-minor-axis ratio. In the example provided in Figure 4 where the ratio is 0.3, it corresponds to a 50% reduction in scan time. 4.4 Discussion Figures 4.2-4.3 indicate that the proposed method is able to achieve anisotropic FOV support using a GA sampling scheme. When the same number of spokes as the fully sampled trajectory are used, the PSFs will exhibit minor side lobes inside the desired FOV, due to the nature of imperfect uniform distribution of GA spokes, especially when the number of spokes per frame is small and/or not a Fibonacci number. In applications where undersampling is not desired, the maximum azimuthal gap for conventional GA has been calculated in [56]: Δθ max (N ga ) = g(1−g) i−1 π F (2i)≤N ga <F (2i + 1) (1−g) i π F (2i + 1)≤N ga <F (2i + 2) (4.6) 41 conventional GA with circular FOV proposed GA with rectangular FOV proposed GA with elliptical FOV 34 spokes 34 spokes 55 spokes Figure 4.5: Comparison of long-axis cardiac images with different FOV shapes. Real-time acquisition with breath-hold were used for all images. Top: diastolic frame with 34 spokes reconstructed with gridding using conventional GA, proposed GA with rectangular and elliptical FOV (major-to-minor-axis ratio 1:0.4) sampling respectively. The unaliased FOV shapes are shown (white dashed contour) for each sampling scheme. The enlarged region of interest, together with another systolic framearealsoshown. Bottom: twoframesfromthesameacquisitionreconstructed with 55 spokes. The conventional GA cases contain a visibly larger amount of streaking artifact due to undersampling (white arrows). 42 30% 40% 50% 60% 70% 80% 90% 100% 20% 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FOVy/FOVx 50% samples needed if FOV ratio is 0.3 (Fig. 4) Figure 4.6: The benefit of elliptical FOV imaging increases with FOV asymmetry. The plot shows the percentage of data needed for elliptical FOV when compared to circular FOV radial sampling as a function of the major and minor axes ratio, given the same undersampling factor. where g = 2/(1 + √ 5), and F (k) is the Fibonacci number for k> 0. For elliptical FOV, this can be directly applied in the angle-normalized θ 0 space to choose the spoke number that satisfies Δθ max (N ga )/π = Δθ 0 max (N ga )≤ Δθ 0 Nyquist = 1/N (4.7) to avoid undersampling, whereN is the spoke number for the fully sampled trajec- tory determined by the Larson method. In our example (Figure 4.2), this results inN ga = 89, which leads to significant aliasing reduction. The remaining low-level aliasing inside the FOV is likely due to 1) imperfect parametric mapping when piecewise linear interpolation is used; and 2) the finite width of aliasing lobes is not accounted for in the Larson method, as discussed in detail in [65]. Note that 43 aliasing was insignificant (at least∼100x lower than the main lobe in the provided example) and should be negligible for most clinical applications. When Nyquist sampling is not required, as in most of the dynamic GA appli- cations, the proposed method nicely combines the benefits of anisotropic FOV and the GA sampling scheme. Figure 4.2f-g indicates that the PSFs of the proposed trajectories are stable (main lobe) and incoherent (side lobes) over time. This is desired for undersampled dynamic imaging, as it is intrinsically compatible with compressed sensing reconstruction [20]. Figure 4.3 demonstrates that the modi- fied GA sampling is able to maintain the desired spoke distribution for anisotropic FOV for arbitrary window sizes. Similar to conventional GA, optimal results can be obtained when a Fibonacci number is used for the window size. Figure 4.4 shows that the proposed method can significantly reduce streaking artifacts for the same acquisition time when compared to conventional GA. It can also achieve comparable image quality as Larson’s method when Nyquist sampling is satisfied. In vivo results also confirm that less streaking can be observed with the pro- posed method after gridding (Figure 4.5). Because less aliasing needs to be resolved compared to conventional GA sampling, a higher acceleration factor can be expected after combining with parallel imaging and/or constrained reconstruc- tion. Also notice that while both have better performance than conventional GA sampling, the differences between elliptical and rectangular FOV samplings are difficult to detect. This implies that the proposed method is insensitive to small differences in the FOV shape when heavy undersampling is used. The benefit of anisotropic FOV radial imaging increases with FOV asymmetry. For elliptical FOV, it can be expressed as a function of the major-to-minor-axis ratio, as plotted in Figure 4.6. The gain could be most significant in applications 44 such as dynamic contrast-enhanced spine or leg imaging where the major-to-minor- axis ratio can be 1:0.3 or higher. In these applications, time-intensity curves of properties like blood or bone marrow perfusion are often measured [69–71] but the optimal trade-offs between the temporal resolution and SNR for accurate mea- surements are difficult to know in advance. The proposed method not only makes radial sampling much more efficient but also makes such prior knowledge less crit- ical. The optimal temporal resolution can be determined retrospectively. Even in the case of cardiac or abdominal imaging where the ratio is about 1:0.5, a 33% scan time reduction can still be achieved. This is particularly useful for real-time applications where the acquisition window is short and underdamping is inevitable [58, 72]. The piecewise linear interpolation approach should be able to serve as a good approximation for FOV ranges in most clinical applications. In our experience, only in the cases of extremely small and asymmetric FOV (in pixel units), where N < 10 for fully sampled radial trajectory andX/Y > 5, did theR 2 value between the optimal and approximated F −1 (θ) drop below 0.99. In such cases, a higher order spline interpolation can be used. Alternatively, piecewise linear interpolation can always be applied on a larger FOV with the same shape, so thatf(θ) does not change. The proposed method is also compatible with any other sampling scheme that targets uniform spoke density distribution besides golden angle. One example is the recent work on “small golden angles” by Wundrak et. al [73], in which a set of azimuthal angle increments smaller than the golden angle were found to give nearly uniform spoke distributions as long as certain minimum number of spokes are used. This is particular useful to reduce eddy currents in balanced-SSFP radial MRI. 45 Recently the combination of parallel imaging, constrained reconstruction, and conventional GA sampling has become increasingly popular to push the limit of accelerating MRI [58, 72, 74]. The proposed method can be easily incorporated intotheseframeworksandsubstitutetheconventionGAsamplingtofurtherreduce scan time, should they be applied to noncircular FOV imaging. It also requires very light calculations, which can be computed on-the-fly to allow interactive mod- ifications of plane orientation and FOV change. 4.5 Conclusion We have demonstrated a simple solution to enable 2D anisotropic FOV support for golden angle radial imaging. This can reduce imaging times in many scenarios (abdomen, spine, etc.) where the object dimensions are anisotropic, while still allowing for retrospective selection of temporal resolution. It can also be easily extended to 3D stack-of-stars imaging and combined with other acceleration tech- niques to further reduce scan time. 46 Chapter 5 Characterization of MRI Acoustic Noise and Implications for Noise Reduction Acoustic noise, caused by fluctuating gradient magnetic fields, is a significant source of patient discomfort in routine clinical MRI. This issue is more significant at higher field strength [75]. It can reach 95 dBA on average for a 2D scan and can exceed 130 dBA in extreme cases on commercial 3T scanners by our measurement. The noise can be reduced by about 20 dBA with proper ear protection, but would still be as loud as standing next to a vacuum cleaner. This problem becomes more severe for long scans, and for situations where it is desirable for the subject to sleep without sedation during MRI scanning [53, 76]. MRI acoustic noise originates from vibrations of the three pairs of physical gra- dient coils. Because these coils are inside a large static magnetic field (B 0 ), they will experience Lorentz forces when the currents in these coils change (slewing). MRI scans require constant switching of the gradients to generate spatial infor- mation. This leads to constant changes in Lorentz forces, which cause vibrations of the gradient coils. The noise can be heard because these vibrations occur at frequencies within audible range (20 - 20 kHz). Many attempts have been made to characterize and reduce MRI acoustic noise. These include active noise cancellation during gradient design [77]; inserting a vac- uum layer to isolate vibration propagation [78]; installing extra copper shielding to increase shielding efficacy [79]; analyzing the impact of inserting a gradient coil on vibration with a finite element model [80]; and exploring trade-offs between 47 acoustic noise and field linearity during coil design [81, 82]. An independent linear model was first proposed by Hedeen & Edelstein [83], in which a transfer function relates the input gradient waveform and output acoustic noise on each of the three gradient axes. Several other studies followed this model [84–91]. The transfer functions were measured and used to design “soft” gradients [84] and study B 0 fluctuation caused by gradient coil vibrations [85]. Smink et al. showed the ability to reduce sound pressure level by TR to avoid resonance peaks of the scanner [86]. Schimitter et al. modified slice-select gradient shape to avoid acoustic resonance frequencies [87]. Li et al. demonstrated prediction of the sound of echo planar imaging sequences based on the transfer functions mainly from one physical axis [88]. Shaping and timing of the gradient pulses were both taken into consideration in [89], but the results were still limited to one axis only. Measurements from all three gradient axes were combined and used to predict acoustic noise for differ- ent sequences in [90, 91], but the results showed substantial differences between predicted and recorded sound. The differences were more than 20 dB at some frequencies. In this work, we experimentally evaluate the independent linear model for gradient-induced acoustic noise, by directly testing the superposition and homo- geneity properties. We also introduce a new method to synchronize the measured impulse responses for all gradient axes, and demonstrate significantly improved sound prediction when multiple gradients are used simultaneously. Finally, we examine differences in the measured transfer functions with different subjects and with different microphone locations within the scanner bore for a single subject, and discuss implications on the ability to perform general acoustic noise reduction by avoiding system resonance peaks. 48 5.1 Methods Experimental Methods Experiments were performed on a clinical 3T MR scanner (EXCITE HDxt, General Electric, Waukesha, WI). Gradient waveforms were designed in MATLAB (MathWorks Inc., Natick, MA), based on a maximum amplitude of 40 mT/m, maximum slew rate of 150 mT/m/ms, and sampling period of 4 μs. Gradient waveforms included: triangles, trapezoids, and low-pass filtered random noise. Acoustic noise was recorded using an MRI-compatible microphone (Model 4189, Brüel & Kjær, Nærum, Denmark). We used the highest sample rate (48 kHz) available on the device. Sound pressure level (SPL) was measured using a sound level meter (Model 2250, Brüel & Kjær). Single-Axis Linearity Testing & Transfer Functions Previousstudies[83–91]haveassumedthat, foreachpairofgradientcoils, there is a linear system relationship between the gradient waveforms and the acoustic noise they produced. To our knowledge, this linear relationship has not yet been verified by direct experiment based on the definition of linearity. We begin by directly testing the homogeneity and superposition properties of each axis. LetT{·}bethesystemfunctionwheretheinputg i (t)(i =x,y,z)isthegradient waveform and output y i (t)(i = x,y,z) is the recorded sound. Because Fourier transform (FT) is a linear operator, homogeneity and superposition properties for each axis can be expressed as: FT [T{ag i (t)}] =FT{ay i (t)} =aY i (f) (5.1) FT{T{g i,1 (t) +g i,2 (t)}} =FT{y i,1 (t) +y i,2 (t)} =Y i,1 (f) +Y i,2 (f) (5.2) 49 0.5ms 30 20 10 0 g (mT/m) a 10 0 -10 0.5ms 0.5ms 0 10 20 30 40 50ms 30 20 10 0 30 20 10 0 b c d Figure 5.1: Gradient waveforms used for linearity test and transfer function mea- surement. a)-c) are triangles and trapezoids; d) shows one realization of random noise gradient after low-pass filtering (f c = 4 kHz) and ten different realizations are used. For superposition test, any two of the waveforms are first scaled by 1/2 and then summed to make sure maximum slew rate is not exceeded. The units for these waveforms are all mT/m. whereY i (f) is the sound spectrum ofy i (t) after Fourier transform. We used trian- gle, trapezoidal, and 10 different filtered random noise waveforms as inputs to test system linearity on each gradient axis, as shown in Figure 5.1. All random noise gradient waveforms were low-pass filtered to 4 kHz due to the slew rate limit of the scanner. Homogeneity errorse h and superposition errorse s were calculated by comparing the magnitude of the right and left side of Eqn. 5.1 and 5.2 respectively: e h =|FT{T{ag i }}−aY i |/|aY i | (5.3) e s =|FT{T{g i,1 +g i,2 }}− (Y i,1 +Y i,2 )|/|Y i,1 +Y i,2 | (5.4) If the linearity property holds, we can determine the system transfer functions. We define H i (f) =FT{y i (t)}/FT{g i (t)} =Y i (f)/G i (f) (i =x,y,z) (5.5) 50 as the transfer functions, where f is the temporal frequency variable. We again used the gradients shown in Figure 5.1 as inputs to calculate H i (f) for each axis respectively. Acoustic Noise Prediction The measured transfer functions can then be combined to predict acoustic noise of arbitrary gradient sequence: b Y (f) =G x (f)H x (f) +G y (f)H y (f) +G z (f)H z (f) (5.6) where G i (f) are the frequency spectra of input gradient waveforms. One problem with the prediction arises from errors in the calculation ofH i (f). It is very difficult to accurately identify the exact beginning of y i (t) that cor- responds to a particular g i (t) due to background noise. Because each H i (f) is calculated individually, the relative time delays between the beginning of input g i (t) and outputy i (t) for each axis are different. This leads to different time shifts of the impulse responses for different axes, which is equivalent to applying differ- ent linear phases to different H i (f). These different time shifts, if not corrected, will cause substantial complex sum errors when using Eqn. 5.6. We propose the following method to resolve this issue: Thebeginningoftherecordedsoundwaveformforeachaxisy i (0)isfirstselected by visual inspection or simple amplitude thresholding. Assume the difference between y i (0) and the actual time the first sound wavefront caused by gradients 51 arriving the microphone is Δt x , Δt y and Δt z respectively for all three axes, Eqn. 5.6 becomes: b Y (f) =G x (f)H x (f)e −j2πfΔtx +G y (f)H y (f)e −j2πfΔty +G z (f)H z (f)e −j2πfΔtz =e −j2πfΔtx [G x (f)H x (f)+ G y (f)H y (f)e −j2πf(Δty−Δtx) +G z (f)H z (f)e −j2πf(Δty−Δtx) ] (5.7) The exact values of Δt x , Δt y and Δt z are difficult to determine, but if ally i (t) used to calculate H i (f) are aligned so that Δt x = Δt y = Δt z , Eqn. 5.6 is reduced to: b Y (f) =G x (f)H x (f)e −j2πfΔtx +G y (f)H y (f)e −j2πfΔty +G z (f)H z (f)e −j2πfΔtz =e −j2πfΔtx [G x (f)H x (f) +G y (f)H y (f) +G z (f)H z (f)] (5.8) The linear phase term at the beginning of the right hand side of Eqn. 5.8 would have no effect on the magnitude spectrum of b Y (f) and would only cause a time shift of its corresponding time domain signal b y(t). We use the following method to align Δt x , Δt y and Δt z , as described in Figure 5.2 as well. Arbitrary gradient inputsareplayedsimultaneouslyonbothx−andy−axes. Anextraterme −j2πΔt is applied toH y (f) to compensate for the difference between Δt x and Δt y . The goal is to find out Δt. Input spectraG x (f) andG y (f) are multiplied by corresponding transfer functions and summed to produce predicted sound b Y (f, Δt). This is then compared with the recorded sound spectrum Y (f) using Itakura-Saito Distance: D IS ( b Y,Y ) =||Y/ b Y = log Y/ b Y − 1k 1 [92]. The smaller the distance of the two spectra, the more similar they are. If Eqn. 5.8 holds, there should be one single 52 1 0 -5 0 5 ∆t (ms) Y xy (f, t) G x (f ) G y (f ) H x (f )e j2 f t x H y (f )e j2 f t y + e j2 f t prediction Y xy (f ) recording Itakura-Saito Distance vary ∆t argmin(I-D dist) = ∆t - ∆t x y ∆t Figure 5.2: Correction of time shifts for x- and y-axis impulse responses. An extra term e −j2πΔt is applied to H y (f) to compensate for Δt x − Δt y . Input spectra G x (f) and G y (f) are then multiplied with corresponding transfer functions and summed to produce predicted sound b Y (f, Δt). b Y (f, Δt) is compared with the recorded sound spectrum Y (f) using Itakura-Saito distance while varying Δt. Δt corresponding to the minimum Itakura-Saito distance is chosen as the estimate of Δt x − Δt y and applied to future sound predictions. minimum ofD IS among different Δt. Thus the Δt corresponding to the minimum of Itakura-Saito Distance should be the difference between Δt x and Δt y . The same procedure is used to align Δt x and Δt z . After the different time shifts of transfer functions are aligned, we then use Eqn. 5.8 to predict the sound. We did experiments in two situations: 1) only one of the three gradient axes was on; 2) all three gradients were on. The predictions were then compared to the measured acoustic noise. For comparison, we also calculated the predicted spectra with no time-shift correction being applied. All experiments above were conducted at a fixed location near isocenter when the scanner was empty. 53 Dependence on Body Habitus and Microphone Location We also investigated the impact of body habitus and microphone location on the transfer functions, as this would be critical for implementing a general method ofreducingacousticnoise, e.g., onethatisbasedonavoidingresonancepeaksofthe system [86, 87]. We measured the transfer functions when two different subjects were inside the scanner. The microphone was placed at the same location, close to the subject’s left ear. Then we moved the microphone along the axis of the bore (z-axis) with a distance increment of 5 cm, and measured transfer functions for each gradient axis. 5.2 Results Single-axis Linearity Tests & Transfer Functions Figure 5.3 shows a representative example of the system homogeneity and superposition test, in which two different random noise gradients were used as inputs on the x-axis. The sound pressure waveforms were measured in Pascal. After applying Fourier transforms, which are integrals over time, the units become Pa sec. Table 5.1 summarizes the results for all three axes. Homogeneity and superposition errors were within 3% for all axes, although errors for the z-axis were slightly higher. Different input gradients shown in Figure 5.1 were used to generate transfer functions. Figure 5.4a-c shows calculated transfer functions for each axis respec- tively. Note that the measured transfer functions did not vary with the choice of input gradient. We show the results up to 2200 Hz for the trapezoid inputs because the trapezoids we used have a full-width-half-maximum (FWHM) of 0.4 ms, which corresponds to their first zero crossing at 2500 Hz in frequency domain. Since 54 Homogeneity Error e h (%) Superposition Error e s (%) g x 0.52±0.13 0.62±0.16 g y 0.48±0.11 0.64±0.15 g z 0.77±0.25 2.77±0.55 Table 5.1: Homogeneity & superposition property test for each physical gradient axis. e h =|FT{T{ag i }}−aY i |/|aY i |;e s =|FT{T{g i,1 +g i,2 }}−(Y i,1 +Y i,2 )|/|Y i,1 + Y i,2 |. The input gradient waveforms used are shown in Figure 5.1. a was arbitrarily chosen as long as within system slew rate limit. 0 5 10 15 20 25 30 35 40 45 50 -10 5 0 5 10 0 500 1000 1500 2000 2500 3000 3500 4000 0 5K 10K 0 500 1000 1500 2000 2500 3000 3500 4000 0 2K 4K 6K g x,1 (t) g x,2 (t) time (ms) frequency (Hz) frequency (Hz) mT/m Pa sec Pa sec 2 |Y x,1 (f ) |Y x,1 (f )+Y x,2 (f ) FT{T{2g x,1 (t)}} |FT{T{g x,1 (t)+g x,2 (t)}} a) b) c) | | | | | Figure 5.3: One example of system homogeneity and superposition property test. a) shows the actual random noise input gradient waveforms played after low-pass filtering. Y x,1 (f) and Y x,2 (f) are the recorded sound spectra for input g x,1 (t) and g x,2 (t) respectively. b) shows homogeneity property test result based on Eqn. 5.1 (a = 1/2). c) shows superposition property test result based on Eqn. 5.1. The units for recorded sound pressure waveforms are Pascals (Pa), and the units for their spectra, as shown, are Pa sec. 55 Hz Hz H (f) (dB) y H (f) (dB) z Hz H (f) (dB) x -10 0 10 -20 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 a) b) c) -10 0 10 -20 -10 0 10 -20 Figure 5.4: Transfer functions of all three axes. a-c show transfer functions for x-, y-, and z-axis respectively using different gradient inputs. The colors correspond to waveforms in Figure 5.1. Transfer functions generated by random noise inputs were averaged over 10 different realizations. The magnitudes were referred to 0.1 Pa/(mT m −1 ) as 0 dB. Note that transfer functions generated by two trapezoids were shown up to 2200 Hz due to their FWHM limits. H i (f) =Y i (f)/G i (f), for any frequencies close to the zero crossings of G i (f), the value of H i (f) would not be accurate. For the same reason, we show the spectra up to 4000 Hz for the triangle input, which has its first zero crossing at 5000 Hz. Acoustic Noise Prediction Table 5.2 summarizes our acoustic noise prediction results for each of the single axis as well as the situation where gradients were played simultaneously on all 56 Prediction Error (%) Prediction Error (%) (subject mismatch) Prediction Error (%) (location mismatch) g x 0.41±0.14 14.97±5.95 45.22±15.32 g y 0.61±0.22 15.23±4.68 35.25±18.38 g z 2.76±1.37 29.36±8.63 32.72±8.32 g x +g y +g z 31.90±6.15 34.52±10.73 48.36±19.57 g x +g y +g z (with time shift correction) 3.86±2.49 30.11±9.29 45.36±13.77 Table 5.2: Acoustic noise prediction using the independent linear model. Predic- tion error was calculated using power spectrum difference: (| b Y| 2 −|Y| 2 )/|Y| 2 × 100%. Subject mismatch prediction: transfer functions measured when subject 2 was present was used for subject 1. Location mismatch prediction: transfer functions measured at one location was used to predict sound at a different location 5 cm away along z-axis. axes. Fifteen different inputs were used for each case. The predicted spectra were compared to the actual recorded sound and prediction error was calculated using power spectrum difference: (|Y| 2 −|Y record | 2 )/|Y record | 2 × 100%. Two examples of prediction results are plotted in Figure 5.5. Figure 5.5a shows the case when a random noise waveform was played on y-axis only. Figure 5.5b compares the recorded and predicted sound spectra when different random noise gradients were played on all three axes. All random noise waveforms lasted 50 ms and TR was set to 100 ms. All results were averaged over 10 TRs. Dependence on Body Habitus and Microphone Location The transfer functions were also measured at a fixed location close to isocenter when two different subjects were present inside the scanner, as plotted in Figure 5.6. Transfer functions for four different locations next to the same subject’s left ear were shown in Figure 5.7. The variations show random patterns that are difficult to model. To quantitatively see the impact, transfer functions measured for subject 1 were used to simulate acoustic noise when subject 2 was present; 57 recorded predicted |Y(f)| dB |Y(f)| dB recorded predicted b recorded predicted (phase correction) predicted (no phase correction) a) b) Hz 500 1000 1500 2000 2500 3000 3500 4000 Hz 500 1000 1500 2000 2500 3000 3500 4000 0 40 -10 30 20 10 0 40 30 20 10 Figure5.5: Examplesofpredictedacousticnoisespectrumcomparedwithrecorded sound spectrum. a) a low-pass-filtered random noise (f c = 4 kHz) was played on y- axis only. b) different random noise gradients were played on all the three axes. All random noises waveform lasted 50 ms and TR was set to 100 ms. All results were averaged for 10 TRs. Spectrum 0 dB reference was set to 1 Pa s. The arrow points at the high-energy frequency range where the prediction without phase correction has substantial error. transfer function measured at one location were used to simulate sound at another location 5 cm away. The results are summarized in Table 5.2. 5.3 Discussion We have tested the independent linear model for acoustic noise on a conven- tional MRI scanner, based on the definition of homogeneity and superposition. Our results show that this is a reasonable assumption (error < 3%), especially for 58 0 500 1000 1500 2000 2500 3000 3500 4000 -20 -10 0 10 0 500 1000 1500 2000 2500 3000 3500 4000 0 10 0 500 1000 1500 2000 2500 3000 3500 4000 0 10 Hz Hz Hz no subject subject 1 subject 2 -20 -10 -20 -10 H (f) (dB) y H (f) (dB) z H (f) (dB) x Figure 5.6: Transfer functions for an empty bore and two different subjects. The microphone was placed at a fixed location close to scanner isocenter for all three cases. 0 dB = 0.1 Pa/(mT m −1 ). g x andg y , where the errors are less than 1%. This is in accordance with our single axis sound prediction results. As can be seen in Table 5.2, the power spectrum error for theg z -only case is slightly larger than for the other two axes. This may be related to the geometric assembly of the gradient coils within the scanner, which is beyond the scope of this work. But even so, the linear model is still reliable in general for each gradient axis. From Figure 5.4, it can be seen that for each axis, 59 0 500 1000 1500 2000 2500 3000 3500 4000 -20 -10 0 10 -20 -10 0 10 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 mic location Hz Hz Hz 5cm -20 -10 0 10 H (f) (dB) y H (f) (dB) z H (f) (dB) x Figure 5.7: Transfer functions of different microphone locations. The microphone was placed close to the subject’s left ear and then moved along z-axis with an increment of 5cm. 0 dB = 0.1 Pa/(mT m −1 ). the transfer functions were input-independent, which again supports the linearity of the system. Eqn. 5.6 considers the acoustic noise produced by each pair of gradient coils to be independent. In other words, it assumes that there is no mechanical coupling between the coils. The accuracy of this linear model depends on how the scanner is manufactured and the impact of mechanical coupling could vary among different scanner models. 60 Previous works [84, 90, 91] reported poor accuracy of the prediction methods when sound from all three gradient axes is combined. We suspect that this is in large part due to the different time shifts of the transfer functions. We thus proposed a new method to align these time shifts, as mentioned in the methods section. The prediction accuracy is substantially improved to better than 96% (Table 5.2). This also suggests the impact of mechanical coupling of all gradient coils is minimal in our case and the sound generated from each gradient axis can be simply added without considering the interference between its sources. One could argue that if a triggering device is used, the gradient pulses and sound recording can be started simultaneously. We found that the final prediction is extremely sensitive to even the smallest timing error. If any of the y i (t) used to generate transfer functions was mismatched by even 2 audio samples (0.04ms), the final prediction error increased from <3% to >10%. The triggering input on our research-grade sound level meter had timing accuracy of 500 ms. A triggering device would only work if its accuracy could achieve the level of 0.01 ms or less. It is worth noting that in Figure 5.5, after time shift correction, there are more errors in the lower (<300 Hz) and higher frequencies (>2800 Hz) than the frequency range between them. The lower frequency range corresponds to the wavelengths longer than 1m, which is roughly the length of the bore. So the errors may be due to the non-linear interference such as diffraction. Errors in higher frequency range may be due to increased sensitivity to phase. Most of the acoustic noise energy lies between 500 and 3000 Hz, which is the frequency range where the model predictions are very accurate. Another interesting finding is that the prediction error is higher (∼ 7 %), when maximum slew rate was used on all three axes simultaneously. If maximum slewing does not occur at the same time or is not used, the error is roughly 3%. 61 With the knowledge of the transfer functions, a natural extension would be to optimize the sequence gradients to avoid the system resonance peaks so that the acoustic noise can be reduced. However, this may be difficult to implement. As we can see from Figure 5.6 and 5.7, the transfer functions vary greatly among different subjects and microphone locations, especially for frequencies higher than 1000 Hz. Table 5.2 also shows substantial prediction errors if the exact transfer functions are not used. Due to the nature of sound wave propagation and the irregular shape of scanners, the variation is difficult to model. Even if the acoustic noise at a particular location can be reduced, unless both the table and the subject are still throughout the exam, or the gradient sequence is designed such that most of the energy is located at frequencies below 1 kHz, it would be difficult for the subject to benefit. 5.4 Conclusion We have evaluated an independent linear model for gradient-induced MRI acoustic noise on a commercial 3T scanner by experimentally testing the super- position and homogeneity properties. The results show that the errors are less than 3% for all physical gradient axes, and less than 4% when all physical gradient axes are on simultaneously. We introduced a new method to synchronize measured acoustic impulse response for the three axes that improved prediction error from 32% to 4% in when all gradients are on simultaneously. Finally, we demonstrated that the gradient-sound transfer functions are highly dependent on body habi- tus and microphone location within the scanner bore, suggesting that any general approaches for acoustic noise reduction based on avoiding system resonance peaks will likely require subject-specific and location-specific calibration scans. 62 Chapter 6 Minimum Field Strength Requirements for Proton Density Weighted MRI MRI is one of the most powerful imaging modalities, and has had a significant impact on healthcare [93]. MRI is safe, non-invasive, non-ionizing, and is capable of resolving tissues in three dimensions while providing several different types of tissue contrast in a single examination. MRI has two notable limitations, cost and speed. These are highly relevant in an era where rising healthcare costs [94] have placed greater pressure on determining and optimizing the cost-effectiveness of imaging for specific clinical questions. To date, standard clinical MRI (1.5 T/3 T) has proven to be cost-prohibitive for many potential screening and preventative medicine applications. Even for diagnostic applications, achieving better image quality without improving outcomes, at the expense of reducing access due to high cost, can be only counterproductive [95]. On the other hand, low-field MRI (≤ 0.5 T) can be much less expensive while still maintaining equivalent diagnostic values for certain applications, as demonstrated by Rutt et al. [96]. Several technological developments have helped to address the speed and tem- poral resolution of MRI scanning. Fast gradients and parallel imaging have had a significant impact and are now available on almost all commercial MRI scanners. Constrained reconstruction [97] and compressed sensing [20] are emerging tech- niques that provide the potential added benefit of de-noising. These technological advances are typically developed and tested first on high-field scanners, defined here as≥1.5 T. 63 The purpose of this work is to provide a framework for determining the mini- mum field strength requirements of novel MRI methods. Due to the difficulties in differentiating different species in k-space, the current framework is most appro- priate for proton-density weighted (PDw) acquisitions. Using this tool, researchers could determine the relevance and applicability of their techniques at lower field strengths (e.g. 0.1 to 0.5 T) even if they have only had the opportunities to test them at high field strengths (e.g.≥1.5 T). When applied to de-noising techniques and constrained reconstruction, this could also enable researchers to determine if their techniques could enable a reduction in the cost of MRI, should such instru- ments be designed for their applications. In this manuscript, we provide phantom validation of this framework, and provide two illustrative examples of how to pre- dict minimum field strength requirements. The first example application is real-time upper airway imaging, for the assess- ment of sleep-disordered breathing. The lack of anatomical information is a major limitation for current sleep studies, and dynamic MRI has been shown [46, 53, 54, 98, 99] to be an promising method to fulfill this unmet need. The high cost associated with conventional clinical MRI scans is arguably the number one reason that prevents these methods from being applied to routine sleep studies. If the scans can be performed on low-field scanners at much lower cost, the option of including MRI in sleep studies will be much more realistic. Besides lower cost, reduced Lorentz force experienced by the gradient coils and hence lower acoustic noise is another attractive feature of low-field MRI, especially for imaging during sleep. The second example application is the measurement of liver fat fraction. Con- ventional high-field MRI has proven to be a powerful tool for body and organ fat distribution assessment [100, 101] and for tissue fat fraction quantification [102]. 64 It has the ability to resolve all fat depots and to measure organ fat. As obesity prevalence continues to rise, there is increasing need of accurate and low cost tools for assessing and quantifying body fat distribution including organ fat. If fat- water separated MRI can be performed at a much lower per-scan-cost, it could become the most cost-effective technique to address body composition assessment in preventative medicine. 6.1 Theory & Methods Modeling Assumptions To simulate low-field acquisition from data acquired at high field strength, we make six assumptions, listed in Table 6.1, and explained below. (1)Body noisedominance. Weassumethatbodythermalnoiseis thedominant noise source at all field strengths under investigation (0.1 - 3.0 T). The validity of this assumption depends on field strength, imaging volume and the receiver coil. It has been shown that body noise dominance can be achieved at frequencies as low as 4 MHz in system sizes compatible with human extremity [103, 104], suggesting the feasibility of performing most human scans with body noise dominance at 0.1 T or above. (2) Consistent B + 1 field. We assume that the uniformity of RF transmission is consistent across field strengths. Since the RF operating frequencies go down at low field, the flip angle variation is expected to be smaller in real low-field imaging compared to our simulation. (3) Consistent B − 1 field. We assume that the receiver coils have the same geometry and noise covariance at different field strengths. In order to simulate 65 • Body noise dominance • Consistent RF transmit field (B + 1 ) • Consistent RF receive field (B − 1 ) and noise covariance (Σ) • Consistent B 0 homogeneity • Single species dominance or PDw • Steady state acquisition Table 6.1: Assumptions for low field simulation. arbitrary B − 1 field, it would require accurate coil maps and noise covariance at both acquired and simulated fields, which one may not have. (4) Consistent B 0 homogeneity. We assume the same off-resonance in parts- per-million (ppm) at different field strengths. This results in less off-resonance in Hz at lower field. (5) Single species dominance or PDw. We use a single global relaxation correc- tionfunctiontoaccountforthesignalchangeatdifferentfieldstrengths. Becauseit is difficult to separate different species from k-space data, this assumption requires similar relaxation patterns at different field strengths for anything that contributes a significant portion to the signal in the region of interest. Although it may be unrealistic for some applications, this restriction can be relaxed in certain cases. For PDw imaging, the simulation is still valid when multiple major species are present (see Appendix B for details). (6) Steady state acquisition. If the signals are not acquired at steady state, the magnetization relaxation will be determined not only by the sequence parameters but also by the initial state. As a result, a single global relaxation correction cannot be applied and a more complicate time-depend function would need to be calculated. 66 Simulation of Low Field Acquisition The process for simulating low-field data from high-field acquired data is illus- trated in Figure 6.1, and described here. The acquired high-field k-space data can be written as: y h =s h +n h (6.1) where s h and n h are pure signal and noise respectively. Under body noise domi- nance, both the real and imaginary parts of the k-space noise n h can be modeled as multivariate normal distributions: Re{n h }∼N(0, Σ), Im{n h }∼N(0, Σ), (6.2) where Σ∈R k×k is the noise covariance matrix for a k-channel receiver coil and is easily measured by data acquisition with RF turned off. Since the thermal noise variance is proportional toB 2 0 and readout bandwidth BW, the simulated noise ˆ n l at low field becomes: Re{ˆ n l }∼N(0,a 2 bΣ), Im{ˆ n l }∼N(0,a 2 bΣ), a = B 0,l B 0,h , b = BW l BW h (6.3) where l and h stand for low and high field respectively. The pure k-space signal at low field can be modeled as: ˆ s l =a 2 fs h (6.4) where f is a function that represents the signal change due to different relax- ation behaviors at different fields. This can be determined with knowledge of the sequence parameters and the dominant species’ relaxation times. The details of 67 y h normal acquistion n h NO RF acquistion High Field field strength correction relaxation correction f a 2 = (B 0,l /B 0,h ) 2 a 2 f y h noise covariance simulate additional noise n add ~ N(0,[a 2 b - a 4 f 2 ]Σ) Σ= n add + y l Low Field simulated acquistion Figure 6.1: Simulation of low-field k-space data. High-field k-space data y h and pure noisen h are first acquired and served as input. y h is then scaled bya 2 and f to account for signal magnitude change and different relaxation behaviors at different field strengths. f can be determined based on steady state signal equations for different types of sequences (see Appendix B for details). To simulate low-field data ˆ y l , additional noise ˆ n add , as calculated in the text, is added to compensate for the different noise levels. calculatingf for common sequences are provided in the Appendix B. Givenf, the simulated low field k-space data can be written as: ˆ y l = ˆ s l + ˆ n l =a 2 fs h + ˆ n l (6.5) we can rewrite it as: ˆ y l =a 2 fy h + ˆ n add (6.6) where ˆ n l = ˆ n add +a 2 fn h , and from Eqns.6.2 & 6.3, we have Re{ˆ n add }∼N(0, (a 2 b−a 4 f 2 )Σ), Re{ˆ n add }∼N(0, (a 2 b−a 4 f 2 )Σ) (6.7) 68 Phantom Validation To validate the proposed framework, a standard resolution phantom was scanned using a product sequence on 1.5T, 3T, and 7T whole body scanners, all from the same manufacturer (General Electric, Waukesha, WI). T/R birdcage head coils (30 cm diameter) were used at all field strengths. The 1.5T and 3T coils were single-channel. The 7T coil has two receive channels with nearly identical sen- sitivities; data from only one channel was used. The same acquisition parameters were used on all three scanners: 2D FSPGR with 62.5% partial k-space acquisition; FA 10 ◦ ; TE/TR 3.1/10 ms; BW 31.25 KHz; FOV 25.6 cm; matrix size 256×160; thickness 5 mm. T1 and T2 values were measured using inversion recovery SE and SE sequence respectively. Homodyne reconstruction [105] was performed for all images. Real-time Upper Airway Imaging in Sleep Apnea For sleep apnea patients, airway compliance is measure of muscle collapsibility. This involves ultrafast 2D axial imaging of the airway and simultaneous airway pressure measurement [98]. During the process, negative pressure is generated by briefly blocking inspiration for one to three breaths. Under these circumstances, airway motion is extremely rapid, requiring about 10 frames per second and mil- limeter resolution. A custom sequence using 2D golden-angle radial FLASH was implemented on the 3T scanner to acquire an oropharyngeal axial slice of one sleep apnea patient with a 6-channel carotid coil. Imaging parameters: 5 ◦ flip angle, 6 mm slice thickness, 1 mm 2 resolution, TE/TR 2.6/4.6 ms, BW 62.5 KHz. A sep- arate scan with RF turned off was performed to calculate the noise covariance. Acquisitions at various low field strengths were simulated using the same imaging parameters. 69 Twenty-onespokeswereusedtoreconstructeachtemporalframe. Conventional gridding [13] was performed on the acquired 3T data and all simulated low-field data. CG-SENSE [57] was also performed with a temporal finite difference sparsity constraint [58]. The NUFFT toolbox [106] was used during algorithm implemen- tation. Fat-Water Separation Fully sampled k-space data were collected using an investigational IDEAL sequence. An 8-channel cardiac receiver coil was used to scan one adult volun- teer at 3 T. Slice thickness 5 mm, TE 1.4/2.3/3.2 ms, TR 9 ms, flip angle 3 ◦ , BW 62.5KHz. To achieve the same phase shift between fat and water, the product of B 0 and TE needs to remain the same. Therefore TE’s were set to be (B 0,h /B 0,l ) times longer when simulated at low fields. Bandwidths were also set to (B 0,h /B 0,l ) times shorter, enabled by longer TE’s. Images were reconstructed using the graph cut field-map estimation method [107] from the ISMRM fat-water toolbox [108]. 6.2 Results Phantom validation Figure 6.2 compares the image acquired at 1.5 T and 3 T, and simulated from 3 T and 7 T. SNR were measured in all cases. For simulated images, the mean and standard deviation of SNR of twenty different simulations were calculated. The difference between simulated and measured mean SNR was less than 8% for all images of the same field strength, which was considered to be good agreement. 70 Real-time Upper Airway Imaging in Sleep Apnea Figure 6.3 shows two representative frames reconstructed at different field strengths, one with the airway partially collapsed (top rows in both a and b), and one with it open (bottom rows). Figures 6.3a-b correspond to gridding and CG- SENSE with temporal finite difference constraint, respectively. All reconstructed frames are also shown in the supporting movie. The SNR becomes worse as field strength goes down, and the airway becomes completely unidentifiable below 0.3 T. With more advanced reconstructions in b, the noise and artifacts are reduced significantly. We then performed airway segmentation on these images based on a simple region-growing algorithm and show, in Figure 6.3c, the average DICE coeffi- cients over 100 temporal frames (3 breaths) at different field strengths. Segmented airways from the 3T images were used as the references. Fifty independent simu- lations were performed at each simulated field strength. Error bars correspond to 95% confidence intervals. In our experience, DICE coefficient > 0.9 is acceptable for this application, suggesting that the minimum field requirement is 0.2 T. Note also that the DICE coefficients exhibit a sharp drop at 0.2 T and the variance increases significantly, implying segmentation failures. Fat-Water Separation Figure 6.4a compares water-only, fat-only, and fat fraction images for a single axial slice at different field strengths. A region of interest (ROI) in the liver is manually selected and figure 6.4b shows the mean and standard deviation of the fat fraction inside ROI, calculated from fifty independent simulations at each field strength. The precision (standard deviation) becomes worse as B0 goes down. The accuracy (mean) deviates significantly at 0.1 T, a result of dominant noise making fat fraction bias towards 50%. Although the accuracy and precision needed for 71 a clinical liver fat biomarker is not yet known [100], once determined, this type of analysis could facilitate determination of the required minimum field strength. For example, if the accuracy and precision needed are both 2%, then this analysis suggests a minimum field strength of 0.3 T would be sufficient. 6.3 Discussion Many new MR imaging and reconstruction methods are developed at centers that utilize state-of-the-art high-field instruments. In addition to advancing per- formance at high field strengths, it is informative to determine the potential to apply these same techniques on more affordable low-field systems. New methods, if translated and implemented on low-field scanners, could enable many applica- tions that are now prohibitive at low field because of insufficient SNR. Low-field MRI has the potential to be more cost-efficient, and has many other attractive properties including reduced acoustic noise and specific absorption rate (SAR), safer for subjects with metal implants, more uniform RF transmission, and less off-resonance for the same part-per-million B0 homogeneity. If the effective SNR can be improved to reasonable levels with the help of advanced imaging and recon- struction techniques, these nice features could further broaden the role of low-field MRI. Itisrelativelystraightforwardtodeterminetheminimumfieldstrengthrequire- ment for new MRI methods under certain circumstances, as listed in Table 6.1. We have demonstrated the process, using modeling assumptions that are widely accepted in the MR community. However, several precautions need to be taken before applying the model here. First, the model assumes the same sequence parameters at all field strengths. It would be natural to pick different parameters 72 at low fields. Second, the model assumes the same scanner geometry and coil geometry. This is also not perfect, since many design constraints change at low fields and they all could impact the magnet and coil layout. Third, the receiver coil noise goes down more slowly than the body noise as field strength goes down [8]. The validity of body thermal noise dominance is questionable for ultra-low field (< 0.1 T) and small volume imaging. Even in the range of 0.1 to 0.5 T, the requirement for suppressing receiver coil noise, although already achievable, is typically higher compared to at high fields. Finally, to achieve reasonable image quality at low fields, constrained reconstruction methods are likely to be involved in many applications. Although powerful, many of these methods have not been extensively validated yet. One needs to be extra careful with them, especially when the depiction of subtle features is important. Although it would be ideal to validate the assumptions and methods on a real low-field scanner, such validation would require the existence of a low-field scanner with very similar geometry, RF coils and sequence implementations as the high- field scanner. To eliminate the impact of these factors, we performed the validation experiment using 1.5T, 3T, and 7T scanners from the same manufacturer with similar geometry and RF coils. To reduce the effects of B1 inhomogeneity and off-resonance, which are particularly severe at 7T, we used a small flip angle (10 ◦ ) and short TE (3.1 ms) relative to T2 (100 ms) so that the validation can mostly reflect the accuracy of the assumptions and methods in this work. The phantom validationresultsexhibitagoodmatchbetweenthesimulationsandmeasurements. It demonstrates that the assumptions we made are reasonable and the simulations based on them can give reliable predictions. We would like to emphasize that due to the nature of MRI, poorer image quality is inevitable at low fields in almost all cases no matter what acquisition 73 and reconstruction techniques are used. But as already been illustrated here and shown in several other low field studies [96, 109, 110], worse image quality does not necessarily lead to less diagnostic value. With that in mind, selecting appropriate evaluation criteria becomes very important when comparing the results at different field strengths. If, for example, the sensitivity and specificity of the useful features are comparable at both high and low fields, then differences in root-mean-square error (RMSE) are likely to be inconsequential. 74 Figure 6.2: Phantom validations of simulated SNR change. The acquired 1.5T/3T/7Timagesandsimulatedimagesfromdataacquiredat3Tand7Trespec- tivelyarelistedforcomparison. MeasuredSNRarealsolistedbelow. Forsimulated images, the mean and standard deviation of SNR of twenty different simulations were used. Contrast was adjusted for better noise visualization. 75 Figure 6.3: Application to upper airway compliance measurement. a) Gridding reconstruction for data acquired at 3 T & simulated at low field strengths. Two temporal frames are shown: one with the airway partially collapsed (top row) and one with it open (second row). Notice the strong noise that makes the airways graduallyunidentifiableasfieldstrengthgoesdown. b)ThesameframesusingCG- SENSE with temporal finite difference sparsity constraint. c) Airways segmented from images using reconstructions in b) are used to calculate the average DICE coefficients over 100 temporal frames (3 breaths) at different field strengths. 3T images are served as references. Fifty independent simulations were performed at each field strength. Error bars correspond to 95% confidence intervals. 76 a) b) Figure 6.4: Application to abdominal fat-water separated imaging. a) Fat-water separated images reconstructed from data acquired at 3 T and simulated at low fields. Top row: water only; middle: fat only; bottom: fat fractions. b) The mean and standard deviation of fat fraction in the ROI at different field strengths. Fifty independent simulations were performed at each field strength. 77 Chapter 7 Concluding Remarks 7.1 Summary This dissertation presents several technological developments that target the application of imaging sleep apnea with MRI. It focuses on the three biggest chal- lenges faced by this particular application: slow acquisition speed, loud acoustic noise, and high economic cost. The following list summarizes my key contribu- tions: • The development of a real-time imaging method that reduce acquisition time by up to 33 times compared to conventional 2DFT imaging. It combines several acceleration techniques: simultaneous multi-slice excitation, non-Cartesian (radial) sampling trajectory, parallel imaging, and compressed sensing reconstruc- tion. The saved acquisition time is used to improve spatial coverage, spatial and temporal resolutions that are needed for accurate airway compliance measurement. Important clinical findings are discovered based on this imaging technique. • The design and implementation of a golden-angle based radial sampling strategy that supports anisotropic FOV. The benefit of this method increases with FOV asymmetry and can reduce 33% scan time when the major-to-minor ratio is 2:1 for elliptical FOV. Both phantom and in vivo cardiac experiments have confirmed the effect of reduced artifacts compared to conventional GA sampling. • The evaluation and improvement of an independent linear model for gradient-induced MRI acoustic noise. The results show that the errors are less 78 than 3% for all physical gradient axes. A new method that synchronizes measured acoustic impulse response for the three axes have improved prediction error from 32% to 4% when all gradients are on simultaneously. The gradient-sound transfer functions are found to be highly dependent on body habitus and location beyond 1 KHz. • The development of a new framework for simulating lower-field acquisitions based on data acquired at a higher field, which takes account both the signal relaxation and noise amplification. To date, standard clinical MRI (1.5/3 T) has proven to be cost-prohibitive for many applications, including imaging sleep apnea, to benefit large-scale population. The simulation framework has demonstrated that comparable diagnostic values can be achieved at B 0 as low as 0.2 T with the methods we used for imaging sleep apnea. Although the techniques described above were originally developed for imaging sleep apnea, there is no reason they are restricted to it. The combined accel- eration method can be applied to any real-time imaging problems with tailored parameters. The anisotropic FOV support GA sampling will be most useful for applications like spine or leg DCE. The acoustic noise model may be used in the subject-andlocation-specificcalibrationscansforanygeneralacousticnoisereduc- tion approaches based on avoiding system resonance peaks. The low-field simula- tion frameworks can be used to determine the minimum field strength requirement for other applications such as body fat quantification. 79 7.2 Future Work and Remarks As mentioned in Chapter 2, the hardware and physiological constraints funda- mentally limit MRI acquisition speed. Therefore acceleration techniques beyond conventional Fourier encoding is one of the most investigated topics for the whole MRI community now and will likely remain so in the foreseeable future. For simultaneous excitation, a better design of the RF pulse may save some time in the excitation phase while achieve the same effect. Other RF based slice encodings like Hadamard encoding are worth investigating as well. There are also potential opportunities when hardware development such as parallel transmission is also combined. For parallel imaging, we used a 6-channel carotid coil for imaging upper airway, which is suboptimal. First, the number of channels is very limited and the coil geometry is not designed for upper airway. If a tailored receiver coil can be used in the future, it is expected that the image qualities can be improved. GRAPPA based techniques may also be explored to combine with iterative reconstructions. For sampling trajectories, other non-Cartesian patterns such as spiral is likely to further reduce scan time. Two of the big challenges are off-resonance due to air-tissue boundaries, and imperfect gradient errors due to the maximum demand. If appropriate corrections can be achieved for both challenges, the scan time is expected to be further reduced with similar or even better image qualities. For reconstructions, constraints may be added to reduce residual artifacts. Although one needs to be cautious about the trade-off between the gain and added computational complexity, which is definitely application dependent. For example, further smoothing of the pharyngeal muscles by adding spatial sparsity constraint may make the images look better but does not lead to more accurate airway seg- mentation. Anotherplaceforimprovementisoptimizationofthecode. Thecurrent 80 MATLAB implementation is relatively slow and inefficient, further optimization and/or a C++ reimplementation is expected to reduce the reconstruction time. Although the gain of applying anisotropic FOV support GA sampling to head andneckdirectlyisnotverysignificant. Theuniquethingofevaluatingsleepapnea is that typically only the airway is the region-of-interest. Therefore, there are great opportunities to combine anisotropic GA sampling with 2D RF excitation. If most irrelevantpartsaresuppressedintheexcitationphase,leavingonlyalongstripthat contains the upper airway in each axial plane, one can then benefit significantly from anisotropic GA sampling. Other than 2D or stack-of-stars, anisotropic GA sampling can also be extended to 3D radial trajectories. Similar to the 2D case idea, a sampling strategy that has nearly uniform spoke distributions in the 3D k-space for arbitrary temporal window, suchas[111], canbeusedtoperforminterpolationonthe3Dfullysampled trajectory. It can also be applied to other dynamic applications that requires ultra- short TE (UTE) if center-out trajectories are chosen. Regardingacousticnoise, althoughitseemsdifficultforthesubjecttobenefitby simply tuning TR based on our investigation, there are still rooms for reduction. A modified sequence that restricts most acoustic energy within 1 KHz may be designed, so that the gradient-acoustic-noise transfer functions are insensitive to body habitus and location variations. Then the subject will experience a more obvious acoustic noise reduction throughout the scans, if the resonance peaks are avoided. MR elastography [112] is another way to measure collapsibility. It has been mostlyappliedtoevaluateliverfibrosis[113,114]todate, butcanalsobepromising if applied to evaluate sleep apnea. I have briefly tried with an existing vibrator designed for liver elastography, but was not very successful. In my experience, a 81 tailored vibrator that can be placed closer to the upper airway (e.g., inside the mouth) is likely to achieve consistent and useful results. Improve sleep quality, in particular improve the diagnosis and treatment of sleep apnea, is important. However, it remains largely neglected by the general public today. 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Hennig, “Is TrueFISP a gradient-echo or a spin-echo sequence?,” Magnetic Resonance in Medicine, vol. 49, no. 2, pp. 395–397, 2003. 93 Appendix A Inverse CDFs of spoke density for anisotropic FOV Elliptical FOV Let a,b be the be the major and minor axes in pixel units: FOV (θ) =ab q a 2 sin 2 θ +b 2 cos 2 θ (A.1) For isotropic resolution, k max (θ) is a constant, therefore f (θ)∝FOV θ + π 2 =ab/ q a 2 sin 2 (θ +π/2) +b 2 cos 2 (θ +π/2) = 1/ s cos 2 θ b 2 + sin 2 θ a 2 (A.2) After normalization (i.e., integral over [0π) is 1), the normalized spoke density is f (θ) = s cos 2 θ b 2 + sin 2 θ a 2 −1 / Z π 0 s cos 2 θ b 2 + sin 2 θ a 2 −1 dθ (A.3) The angle fori th GA spoke is given byθ[i] =F ( − 1)(θ 0 [i]),F (θ) is the cumulative distribution function: F (θ) = Z θ 0 f (θ)dθ = ab s (a 2 −b 2 ) cos (2θ) +a 2 +b 2 a 2 F ellip θ|1− b 2 a 2 ! A q (a 2 −b 2 ) cos (2θ) +a 2 +b 2 (A.4) 94 where A = R π 0 s cos 2 θ b 2 + sin 2 θ a 2 −1 dθ, F ellip is the elliptic integral of the first kind, and cannot be calculated analytically. Therefore F −1 cannot be expressed analyt- ically either. Rectangular FOV Let a, b be the long and short sides of the rectangle in pixel units, similar to elliptical FOV, the normalized spoke density is: f (θ) = b/ (2A cosθ) θ∈ [0,θ 1 ) a/ (2A sinθ) θ∈ [θ 1 ,π−θ 1 ) −b/ (2A cosθ) θ∈ [π−θ 1 ,π) (A.5) where θ 1 = atan(a/b), A = R π 0 f (θ)dθ = F 1 (θ 1 ) + F 2 (π−θ 1 )− F 3 (π)− F 3 (π−θ 1 ), F 1 (θ) = b 2 log sin θ 2 + cos θ 2 ! − log cos θ 2 − sin θ 2 !! , F 2 (θ) = a 2 log sin θ 2 ! − log cos θ 2 !! , F 3 (θ) =−F 1 (θ). The cumulative distribution function becomes: f (θ) = F 1 (θ) θ∈ [0,θ 1 ) F 1 (θ 1 ) +F 2 (θ)−F 2 (θ 1 ) θ∈ [θ 1 ,π−θ 1 ) F 1 (θ 1 ) +F 2 (π−θ 1 )−F 2 (θ 1 ) +F 3 (θ)−F 3 (π−θ 1 ) θ∈ [π−θ 1 ,π) (A.6) Although F (θ) has a close form solution, F −1 cannot be expressed analytically. 95 Appendix B Signal Relaxation at Lower Field for Common Sequences Spin echo (SE/FSE/TSE) At steady state, the magnetization after excitation can be expressed as M ss =M 0 1−E 1 1−E 1 cosθ sinθ (B.1) where M 0 is the longitudinal magnetization, θ is the flip angle and E 1 =e −TR/T 1 . The acquired signal is s =A (1−E 1 ) sinθ 1−E 1 cosθ e −TE/T 2 (B.2) where A is a constant proportional to B 2 0 . Because T2 is largely independent of field strength [8, 115], we neglect the differences of transverse relaxation due to T2 change at different field strengths. According to Eqn. 6.4, the relaxation correction function becomes f = ˆ s l a 2 s h = " (1−E 1,l ) sinθ l 1−E 1,l cosθ l / (1−E 1,h ) sinθ h 1−E 1,h cosθ h # e −(TE l −TE h )/T 2 (B.3) l and h stand for low and high field respectively. For PDw imaging, where a) TE T2 and b) TR T1 or the flip angle θ is low, f≈ sinθ l /sinθ h regardless of the species type. As a result, the restriction of single species dominance can be relaxed and the equation above can be applied to multiple species types. 96 Gradient echo (GRE/FGRE/SPGR/FLASH) The signal change is similar to spin echo, except following T2 ∗ decay: f = ˆ s l a 2 s h = " (1−E 1,l ) sinθ l 1−E 1,l cosθ l / (1−E 1,h ) sinθ h 1−E 1,h cosθ h # e −(TE l /T 2 ∗ −TE h /T 2 ∗ ) (B.4) In practice, one may not know the explicit values of T2 ∗ , since it also depends on local B 0 inhomogeneity and susceptibility. Given [9] 1 T 2 ∗ = 1 T 2 +cγΔB ppm B 0 (B.5) where c is a constant and ΔB ppm is the field inhomogeneity in parts-per-million. We can rewrite the exponential term in B.4 as: e −(TE l /T 2 ∗ −TE h /T 2 ∗ ) =e −(TE l −TE h )/T 2 e −cγΔBppmB 0 (B 0,l TE l −B 0,h TE h ) (B.6) In cases where T2 ∗ is difficult to estimate, T2 may be used instead of T2 ∗ . As long asB 0,l TE l ≤B 0,h TE h , this will lead to an underestimation of signal, which means the simulated SNR will be at best the same as the actual low-field acquisition. In the airway example, T2 ∗ is unknown, so T2 is used instead. Given proton density weighting and θ l = θ h , f ≈ 1. In the fat-water example, in order to generate the same fat-water phase shift, the product ofB 0 TE needs to remain the same, B.6 is reduced to e −(TE l −TE h )/T 2 . Since small flip angles θ l = θ h = 3 ◦ were used, f≈e −(TE l −TE h )/T 2 , with liver T2 set to 42 ms [8]. Balanced steady-state free precession (bSSFP, FIESTA, true FISP) 97 The steady state transverse magnetization, assuming TE, TR ll T1, T2, is [116]: M ss =M 0 sinθ 1 + cosθ + (1− cosθ)(T 1/T 2) (B.7) based on similar calculations in SE, f is now a function of T1, T2 and flip angle: f = 1 + cosθ + (1− cosθ)(T 1 h /T 2) 1 + cosθ + (1− cosθ)(T 1 l /T 2) (B.8) Inversion recovery (STIR, FLAIR) Following similar analysis, with 90 ◦ excitation, we have: M ss =M 0 (1− 2e −TI/T 1 +E 1 ) (B.9) f = h (1− 2e −TI l /T 1 l +E 1,l )/(1− 2e −TI h /T 1 h +E 1,h ) i e −(TE l −TE h )/T 2 (B.10) Since the inversion time TI is usually chosen to null a particular species, the impact of this species on the signal can be neglected. Here T1 is the value of the remaining dominant species. 98
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Wu, Ziyue
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Seeing sleep: real-time MRI methods for the evaluation of sleep apnea
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sleep apnea
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