NOVEL TECHNIQUES IN PROJECTION-BASED MOTION TRACKING

Transcription

1 NOVEL TECHNIQUES IN PROJECTION-BASED MOTION TRACKING IN CARDIAC MAGNETIC RESONANCE IMAGING by Liheng Guo A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy Baltimore, Maryland January, 2017 Liheng Guo All Rights Reserved

2 ABSTRACT Magnetic resonance imaging (MRI) is indispensable to the medical imaging of the heart because of its ability to manipulate soft tissue contrast, to image both 2D and 3D regions in arbitrary orientations, and its lack of ionizing radiation. These advantages make MRI a highly flexible imaging modality that is used extensively to examine, for example, the heart s congenital defects, myocardial infarctions, vascular perfusion, coronary patency, and contractile performance. However, the heart exhibits constant motion due to cardiac contraction and normal human respiration, both of which lead to significant image corruption, making the heart a particularly challenging target to image. Existing cardiac MRI techniques account for this challenge by using some kind of motion avoidance or motion tracking. Such techniques all incur some degree of cost in terms of imaging efficiency, procedural complexity (e.g. setup of electrocardiogram and respiratory bellows) and/or patient stress (i.e. breath holding). In this work, several new MRI motion-tracking techniques were developed and evaluated. They track cardiac and/or respiratory motion, produce multi-frame cine images or contrast-prepared diastolic images of the heart. A common theme is that they all track motion purely from MR-acquired signals, without external devices, cost to imaging efficiency, or added patient stress. Moreover, they all utilize a particular type of MRI data known as the projections. These techniques were implemented through extensive development of customized MR sequences and the associated post-processing to reconstruct motion-free images. Imaging studies of phantoms, animals, and healthy human volunteers were performed to evaluate the motion-tracking abilities of these techniques. It was found that they produced image quality and cardiac functional measurements comparable to existing MR techniques. These techniques hold significant potentials of enhancing the patient experience, image quality, and imaging efficiency of cardiac MRI in clinical practices. ii

3 Advisor and First Reader: Daniel A. Herzka, PhD Assistant Professor, Biomedical Engineering Johns Hopkins School of Medicine Second Reader: Aravindan Kolandaivelu, MD Assistant Professor, Cardiology Johns Hopkins School of Medicine iii

4 ACKNOWLEDGEMENTS I would like to thank Prof. Daniel Herzka and Prof. Elliot McVeigh for introducing me to the rich and profound field of medical magnetic resonance imaging, which spans a large body of knowledge from physics to signal processing to physiology. I would like to thank them for their confidence and trust in me to take on this challenging subject and for giving me the intellectual freedom to explore, to learn, and to solve problems. Their expertise and guidance have made my Ph.D. a fascinating journey, and their support and enthusiasm have made it an unforgettable experience. I would like to thank my thesis committee, which also includes Aravindan Kolandaivelu, M.D. and J. Andrew Derbyshire, Ph.D. for their continued support and kindness over the past years. It has been an honor to have them to be a defining part of my academic career, and I could not have asked for better imaging scientists. It has been an honor to work with Dr. Kolandaivelu, who is one of the rarest practicing clinicians who are also well versed in MR physics and pulse programming. I would like to thank him for his generous support of my research and his research group for providing access to imaging resources. I have also had the honor to know Dr. Andy Derbyshire for many years, and I have always admired him for his deep expertise in MRI, mathematics, and programming. I would like to thank him for insightful suggestions and cheery attitude; it has always been a joy speaking with him. My gratitude also goes to Prof. Haiyan Ding for her encouragement and guidance, both technical and philosophical, both in research and life. She has been a great mentor of another kind. I would like to thank all my friends for making Baltimore life survivable, and even fun! And also for all embarking on new journeys one after another, reminding me it is time to move on too! I would like to express my special gratitude to J. Hossain, Ph.D., S. Wright, and J. Song, Ph.D. for treating me like family, turning the toughest times into the warmest. Of course, for my actual family, I would like to thank my parents for their great patience putting up with the highs and lows of my Ph.D.; their love is unconditional and independent of accomplishments and setbacks. iv

5 TABLE OF CONTENTS Abstract... ii Acknowledgements... iv Table of Contents... v List of Figures... x List of Tables... xxv 1 Introduction Magnetic Resonance Imaging Signal and Contrast Formation Spatial Encoding and the k-space The 2D Cartesian k-space in Practice Cardiac MRI Overview The bssfp Real-Time Cardiac Imaging Segmented Gated Cardiac Imaging The Standard Segmented Gated Cardiac Imaging Limitations of ECG Gating and Breath Holding External Respiratory Tracking MR-Derived Motion Tracking Center of k-space The Diaphragm Navigator Low-Resolution Images Projections v

6 1.4 Thesis Overview Pseudo-Projection Driven Cardiorespiratory Self-Gated Cardiac Cine Imaging Abstract Introduction Theory Motion Tracking Using Near-Center Cartesian Readouts Golden-Step Phase Encoding The Original Radial Golden Ratio The Cartesian Golden Step Methods Simulation Sequence Imaging Experiments Post-Processing Pseudo-Projection Stream Formation Cardiac Motion Tracking Respiratory Motion Tracking Similarity-Based Data Sorting Image Quality Evaluation Results Simulation Pseudo-Projection Formation Cardiac and Respiratory Motion Tracking Self-Gated Cine Quality Discussion and Conclusion Technical Considerations vi

7 Pseudo-randomness Non-Fibonacci Grid Size Pseudo-Projection Formation Limitations Motion Detection Dark Flow Artifact Extensions and Future Work Conclusion Sorted Golden Step Cardiorespiratory Self-Gated Cine Imaging Abstract Introduction Methods Sequence Imaging Experiments Motion Extraction and Cine Reconstruction Image Quality Evaluation Results Motion Tracking Image Quality Discussion and Conclusion Technical Considerations Extensions and Future Work Conclusion Simultaneous T 2 Prep and Respiratory Motion Tracking for Cardiac MRI Abstract Introduction vii

8 4.2.1 T 1 and T T 1-Weighted and T 2-Weighted Imaging T 1-weighted imaging T 2-weighted imaging T 2-Weighted Cardiac Imaging Overview of the Present Work Methods Sequence Phantom Studies Static Phantom Studies Moving Phantom Studies Normal Human Subject Imaging Studies Image Quality Evaluation Swine Studies Results Phantom Experiments Human Subject Experiments Swine Experiments Discussion and Conclusion Technical Considerations Extensions and Future Work Conclusion Conclusion Summary of the Current Work Limitations viii

9 5.3 Future Extensions References Curriculum Vitae ix

10 LIST OF FIGURES Figure 1.1. Example 2D Cartesian k-space, a Cartesian readout, and the gradients to realize the readout. (a) shows a simplified discrete 2D Cartesian k-space with only 16 sample points along both k x and k y (N x = N y = 16), centered on (N x/2+1)-th and (N y/2+1)-th sample point from k minx and k min-y. Superimposed is a single Cartesian readout with N x samples (Segment 2), along with two transitional k-space trajectories (Segments 1, 3) that start and end with the k-space origin as a feature of steady-state imaging. The readout is typically along the k x or frequencyencode direction, whereas k y is known as the phase-encoding direction. Normally, N y readouts at the N y-many equally spaced phase-encode positions are acquired to have the complete k- space data for an image. (b) shows the gradients that realize the entire k-space trajectory, with shaded portions labeled with their corresponding k-space trajectories. Note that the z-gradient is the slice selection gradient along the z-axis, and its k-space trajectory is not visible on a 2D graph of k x and k y. The radiofrequency (RF) excitation pulse is also shown although it does not affect the k-space trajectory. (c) Shows the magnitude of an actual k-space, which corresponds to the imaging slice (d). Because the Fourier transform removes all spatial information from the input signal, any feature in an image is dispersed to all parts of the k-space, and as a result the appearance of the k-space is largely uninformative to the human eyes Figure 1.2. Example of motion in cardiac imaging: An MR image of the cross section of the human heart is seen in (a) where the respiratory motion was avoided by breath holding. When breath holding is unsuccessful or impractical, the respiratory motion causes significant corruption of the image (b). When motion is accounted for by using motion-tracking techniques, which, for example, only accepts imaging data at a single motion state, a clear motion-free image can be obtained despite the presence of breathing motion (c) x

11 Figure 1.3. Comparison of balanced steady state free processing (bssfp) (a) and gradient echo (b) cine frames of the same slice at the same spatial resolution on a 1.5 T MR system. The bssfp image of the heart is superior in terms of blood-myocardium contrast and signal-to-noise ratio. Additionally, bssfp imaging is faster due to its short repetition time (TR): in this example, the cine frame rate is 50% higher than that of the gradient echo. These advantages make bssfp the natural choice for cardiac MR imaging Figure 1.4. The acquisition of a segmented ECG-gated cardiac cine. The cine has N CP cardiac phases or image frames (a). Because the k-space for a single image frame cannot be acquired within the desired temporal resolution (~30ms), the k-space is divided into N seg segments (b), each of which can be acquired at such temporal resolution. The i-th segment is acquired repeatedly (for N CP times) during the i-th heartbeat in a scan, guided by an external ECG (d). After N seg heartbeats, the scan is complete with N CP frames of k-space Figure 1.5. The projection slice theorem: in k-space (a), if a linear measurement passing through the k-space center at is made at a particular angular orientation (c) and inverse Fourier transformed into 1D spatial domain (d), it is the same signal as the original image projected onto a line of the same angle in image domain (b) Figure 2.1. The original use of the golden ratio in radial dynamic MRI. Comparing to conventional angular increments of the radial readouts (a), which covers the angular space sequentially and starts to repeat angles after the first complete rotation, the golden ratio (b) covers the angular space pseudo-randomly. Every additional readout acquired fills in the largest angular gap remaining. Thus the angular space is covered approximately uniformly, and without repetition regardless of number of readouts acquired IEEE. Reprinted, with permission, from Winkelmann et al, An Optimal Radial Profile Order Based on the Golden Ratio for Time Resolved MRI, IEEE Transactions on Medical Imaging, Jan xi

12 Figure 2.2. PE execution order of the golden step scheme, as compared to the sequential and interleaved schemes (a). In the golden step scheme, the Cartesian k y grid with 144 evenly spaced PEs and is covered exactly once by incrementing the PE index by 89 for 144 times. In the interleaved scheme, each segment consists of 8 readouts. The size of the largest gap remaining on the k y grid as a function of acquisition time is plotted (b). The golden step covers the remaining gaps the most quickly among the three schemes, as indicated by its steep dropoff near the start of the scan Figure 2.3. The integer golden-step PE ordering (a c): a Cartesian k y grid with 144 evenly spaced PEs is covered exactly once by incrementing the PE index by 89 with each readout, where 89 and 144 are consecutive Fibonacci numbers. A central subsection of k y is used as the navigator zone (dashed lines), within which the imaging readouts are also to be used for motion tracking. The golden-step PE ordering allows for approximately uniform coverage in time and in k y at any navigator zone width, shown here varying from 5% to 15% in a) through (c). In comparison, another commonly used PE ordering, the interleaved ordering (d f), cannot maintain uniformity since it shows large gaps in coverage in certain navigator-zone widths, as in (d) and (e). (An interleaved acquisition of 144 total PEs and 8 readouts per segment is shown here.) Figure 2.4. Overview of the post-processing chain used in this work to derive motion from pseudoprojections and guide cine reconstruction Figure 2.5. Intensity profiles drawn to evaluate the blood-myocardium sharpness (a, b) and contours drawn to evaluate cardiac function (c) Figure 2.6. Pseudo-projection of 2D solid circular phantoms (a) with diameters of 1/2, 1/4, 1/8, and 1/16 FOV were simulated to undergo sinusoidal motion (b). Their x inverse Fourier transforms of readouts at 0, 1, 2, 4, 8, and 16 Δk y phase encodes were generated (c). Smaller phantoms were found to retain projection appearance until higher phase encodes than did xii

13 larger phantoms, because the Fourier transform of narrower objects are more spread-out in k- space Figure 2.7. Formation of the pseudo-projection stream used for cardiorespiratory motion tracking. One complete coverage of the 144-PE Cartesian k-space (over ~ 375 ms) were acquired using the discrete golden-step phase encode ordering (a). Imaging readouts inside the navigator zone (central 10% of k y) were used for motion tracking, and the magnitude of their inverse Fourier transform, the pseudo-projections, are shown in (b). Imaging data acquisition covered the k- space repeatedly for the entire duration of the scan. The first 1000 raw pseudo-projections (over approx. 28 sec.) are shown in (c), though motion is not immediately recognizable. After magnitude scaling (d) to reduce k y-dependent intensity fluctuation, and smoothing along time (e) to further reduce high-frequency changes, cardiac and respiratory motions are visible in the final form. White arrows mark five cardiac cycles and the black arrows mark two respiratory cycles Figure 2.8. Widths of the navigator zone (a e) and its impact on the pseudo-projection stream (f j) during a free-breathing cardiac scan. The intensity over time of the marked pixels is superimposed on each stream (white). The narrowest navigator zone width would correspond to the conventional projection-based motion tracking using only the k y=0 readout (a, f), which revealed respiratory motion only. As higher-k y PEs were included, cardiac motion started to emerge (2nd, 3rd rows). At a width of 10% k y (d, i), both cardiac and respiratory motions were fully revealed. It resulted in a motion-sampling frequency of 38 Hz and was used to process all scans in this work. Beyond 10%, no additional motion information was revealed and respiratory motion may become degraded. All data shown in this figure originated from the same duration of the same scan, as widths of navigator zone could be freely adjusted retrospectively Figure 2.9. Example of the PCA-based motion extraction from a free-breathing scan. In this example, the 2nd (a) and 3rd (b) most significant eigenvectors of the pseudo-projections xiii

14 covariance matrix predominantly carried respiratory and cardiac motion, respectively (the 1st eigenvector carried DC signal level). The cardiac eigenvector was filtered and a movingaverage-crossing algorithm was applied to generate self-gating events in c. The recorded ECGderived triggers are also shown on (b) and (c) as the timing reference. The filtered respiratory eigenvector is shown in (d), superimposed on the pseudo-projections showing nine cycles of respiratory motion (a respiratory-dominant coil is shown, although all coils were used in motion extraction). Also superimposed is the respiratory gating window around the most frequent position of the waveform, preliminarily accepting 30% of the data. Note that the more irregular portion of the respiratory motion was preserved (first 10 seconds) Figure Timing errors by event type of cardiac self-gating events. Each data point represents a golden-step scan, marking the standard deviation of the timing differences between the automatically detected self-gating events and their corresponding ECG triggers. The lower, middle, and upper edges of each box indicate the 25th, 50th, and 75th percentiles, respectively. In self-gated reconstructions, the type with the lowest event interval variance was used to generate cardiac triggers. Troughs were the least variable and were selected for triggering in 12 out of the 16 scans Figure End-systolic and end-diastolic frames of self-gated cines (GS BH, GS FB) compared to breath-hold ECG references (ECG BH). In both SAX (a) and LAX (b) cines, small features (white arrows) were well resolved in self-gated reconstructions. Golden step acquisitions reconstructed without respiratory gating (GS FB No Resp Gating) show the effects of motion. The motion profiles visualize the time course of intensity over a line segment of the image (dashed). In golden step acquisitions, however, regions of blood flow were prone to signal inhomogeneity or loss, especially in the LAX orientation. (ECG BH: standard prospective ECG-gated breath-hold acquisition; GS BH: golden-step breath-hold acquisition with cardiac self-gating; GS FB: golden-step free-breathing acquisition with both cardiac and respiratory self-gating.) xiv

15 Figure Comparison of cine frames showing eddy current and flow-induced artifact during a cardiac cycle. (a): Reference cine (ECG BH) acquired with sequential PE, ECG gating, and breath hold. (b): golden-step breath-hold acquisition (GS BH) reconstructed using ECG gating and no self-gating. (c): the same GS BH acquisition reconstructed with cardiac self-gating. (d): golden-step free-breathing acquisition (GS FB) reconstructed with cardiac and respiratory self-gating. Compared to the reference, signal disturbance and smearing in and around the cardiac blood pool can be seen in all three golden step acquisitions, particularly in cardiac phases where blood flow is the highest (i.e. columns 2, 5, and 6). Given that similar levels of artifact can be seen in (b) (d) regardless of the motion tracking method, the artifact is most likely independent of self-gating and due to flow effects compounded by eddy currents associated with golden step PE jumps Figure Comparison of sharpness measurements from the golden-step self-gated cines (GS BH, GS FB) and those of the reference cines (ECG BH). An example of sharpness profile placement is shown in (a). In (b), all sharpness measurements made on end-systolic (SYS) and end-diastolic (DIA) frame from SAX and LAX slices are included, categorized only by scan types. Measurements from SAX and LAX slices are separately compared in (c) and (d), respectively, categorized by both scan type and cardiac state. As seen in (c) and (d), the SAX sharpness measurements were slightly greater than LAX, and end-systolic and end-diastolic measurements were comparable. For all box plots, the lower, middle, and upper edge of each box indicate the 25th, 50th, and 75th percentiles, respectively, and the extremes of the whiskers cover the range of data. (GS: Golden-step; BH: breath-hold; FB: free-breathing; SAX: short-axis; LAX: long-axis.) Figure Comparison of functional measurements from golden-step self-gated cines (GS BH, first row; GS FB, second row) and those of the reference cines (ECG BH). Obtained from regions of interests (ROIs) drawn on SAX cines, LV blood pool area (a, b, e, f), LV myocardial area (c, d, g, h), and single-slice ejection fraction (e, i) of the self-gated cines showed good xv

16 agreement with those of the reference cines. Linear regressions (solid black line) are superimposed over the identity line (dashed line). P-values of Bonferroni-corrected t-test are also displayed. For each functional metric, no statistically significant difference was found between self-gated cines and reference cines at a significance level of P=0.05 (Bonferronicorrected). (GS: Golden-step; BH: breath-hold; FB: free-breathing.) Figure Importance of the pseudo-randomness of golden step. A 144-readout golden step acquisition (a) is compared with a 144-readout interleaved acquisition with 8 readouts per segment (d). Their resultant temporal order of navigator zone coverage is color-coded (yellow: the first readout in the navigator zone; red: the last readout in the navigator zone). The wellmixed colors in (b) indicate that the golden step covers the navigator zone in a pseudo-random and uniform manner, resulting in a steady appearance of the cardiac motion on the pseudoprojection stream (c). In comparison, the well-ordered colors in (e) indicate that the interleaved PE ordering covers the navigator zone in a structured way, resulting in a time-dependent, slowvarying change in how motion is transferred onto the projections (f). This inconsistency of appearance would make the detection of motion difficult Figure Mutually Prime PE scheme, where N PE and the jump size have no common factor other than 1, appears to be able to cover the navigator zone at a regular interval (Column 1 and 3). However, many such pairs lead to sequential coverage or large time gaps (Columns 2 and 4). Having to find a pair that results in regular coverage adds burden to pre-scan planning. Also, even when the coverage appears to be regular, it lacks pseudo-randomness and is in fact highly structured, as indicated by the regular patterns in the color-coded timing plots (Row 2). (RO: readout) Figure Adapting the golden step to non-fibonacci k y grid size (N PE): for any desired non- Fibonacci N PE, the next greater Fibonacci number is used to form the k y grid, over which the golden step increment is carried out as usual. During a scan, any k y indices generated that are greater than the desired N PE are simply be skipped. The pseudo-random coverage of the xvi

17 navigator zone is preserved, as indicated by the lack of any regular pattern in the color-coded timing plots (Row 2). (RO: readout) Figure Relative signal magnitude as a function of k y for several subjects. For each subject, all k-space data for each k y value was averaged. The magnitude of the averaged data was normalized to that of the central readout (k y=0). Each color represents a coil, and the thick black curve represents the average of all coils. For most cases observed, the relative signal magnitude drops to 20% at ±5% k y Figure Diagram of phase-encode (PE) gradients for the modeling of extraneous phase accumulation of a moving spin. Three complete TRs are shown. Labels A through B indicate echo times (where spin phase directly affect the image) and refocusing points (where spin phase should be 0). T A is the time interval between the PE and the rewinding gradients within a TR, and T B the time interval between the rewinding gradient of a TR and the PE gradient of the subsequent TR Figure Simulation of extraneous phase on a single spin due to PE-direction flow for several PE schemes. For all schemes (Left Column), the spin is assumed to enter the imaging slice at the first TR and continue to travel at a constant speed along the PE direction. The extraneous phase per unit speed due to PE gradient moments and flow is simulated over the first 30 TRs (blue brackets labeled with sim ) and plotted (Right Column). In the sequential scheme (Row 1), the extraneous phase is minimal. In the golden step and interleaved schemes (Row 2 and 3) where there are large PE jumps, the extraneous phase is significant and causes large phase disturbance from TR to TR Figure 3.1. Comparison of Cartesian phase-encode (PE) schemes. In each row, a Cartesian k y grid with 144 evenly spaced PEs is covered exactly once by a particular PE scheme. In each column, the navigator zone of a specific width (red dashed) selects low-pe readouts for motion tracking (red squares). Row 1: the original integer golden-step scheme provides pseudorandom navigator-zone coverage that is approximately uniform in both time and k y. xvii

18 Row 2 and 3: the golden-step PEs are sorted into temporal segments of 8 and 12, respectively, significantly reducing PE jumps while preserving the pseudorandom coverage of the navigator zone in both time and k y. Row 3 and 4: If a similarly segmented PE scheme like the interleaved scheme were to be used instead of golden step, there would be large temporal gaps in the navigator zone coverage. The motion-tracking readouts would also have temporally structured and slowly varying intensity, causing time-dependent bias in motion measurements Figure 3.2. Comparison of metrics of the golden step (GS), sorted golden step (sgs), and interleaved phase-encode (PE) schemes. Row A: the three PE schemes over time in one complete acquisition of a 144-PE k y space. Row B: PEs inside the navigator zone. Row C: the largest remaining k y gap within the navigator zone over time, note that just like GS, the sgs quickly reduces the gap size, much faster than the interleaved. Row D: cumulative k y of navigator-zone PEs, note that both GS and sgs remain close to k y=0, indicating the symmetric and uniform coverage of the k y interval of the navigator zone. In comparison, the interleaved scheme deviates far from 0 at higher navigator zone widths, suggesting a bias in the sampling of k y, which leads to time-varying depiction of motion. Row E: time intervals between two measurement of the navigator zone, note that the GS and sgs do not have large intervals as does the interleaved, and generally have smaller fluctuation than does the interleaved scheme Figure 3.3. Streams of pseudo-projections for motion tracking. (a) The generation of pseudoprojection streams starts with the normal Cartesian imaging readouts with k y within the navigator zone. To reveal motion, the expected k y-dependent magnitude variation is corrected, and the pseudo-projections are smoothed in time. (b) The effects of segment size and navigator zone width on pseudo-projections: sorted golden step with various segment size are compared to the original golden step at typical navigator zone widths. Both cardiac and respiratory cycles are visible at all practical segment sizes, but generally more clearly at lower navigator zone widths. Note that the streams shown here were processed to prioritize cardiac motion; xviii

19 respiratory motion could also be highlighted using the same data (see the following figure). ROs: readouts Figure 3.4. Cardiac and respiratory motion extraction from pseudo-projections. The central 5% phase encodes (pseudo-projections) were processed for optimal cardiac motion detection (a). From a group of automatically detected cardiac pixels (red + markers), the cardiac waveform was derived and was used to generate cardiac events (b) to replace ECG triggers (dashed, shown for reference). The same pseudo-projections were processed for optimal respiratory motion detection (c), from which a respiratory waveform was extracted using principle component analysis (PCA) to perform respiratory gating (d). In the shown scan, the subject was instructed to breath-hold for several seconds before breathing freely. The flat region at the beginning of (d) shows that non-cyclical motion can be captured. AU: arbitrary Figure 3.5. Comparison of images acquired at various number of readouts per segment. A BSSFP off-resonance band near the imaging slice, which is not observed on the ECG-gated breathhold reference cines (ECG BH, Row 1) due to its sequential PE, caused severe flow artifact (white arrows) with the original golden step (Row 2) due to the compounding effects of large PE jumps and flow. The artifact is significantly reduced when readouts are sorted into segments of ascending or descending PEs (sgs FB, Row 3 5). At more than 4 readouts per segment, the artifact becomes essentially unnoticeable. BSSFP: balanced steady state free precession. PE: phase encode. RO: readout. SAX: short axis. LAX: long axis Figure 3.6. Comparison of the golden step and sorted golden step acquisitions in artifact-prone slices. In some slices of some subjects, the main field inhomogeneity and blood flow are significant enough to compound with the eddy current induced by the original golden step s large phase-encode jumps, forming the dark flow artifact of bssfp (Row 1). However, the same slice can be imaged virtually free of the artifact using the sorted golden step (Row 2, using 12 readouts/segment). The sorted golden step has dramatically reduced, if not entirely xix

20 eliminated, the artifact in all problematic slices encountered in this study. Four such slices from three subjects are shown here Figure 3.7. Visual comparison of cine image quality. Eight frames from a 24-frames free-breathing ECG-free self-gated sorted golden step cine (sgs FB) acquired with 12 readouts per segment are compared with the references cine (ECG BH) acquired with ECG gating, breath hold, and sequential PEs (also 12 readouts per segment). Several representative slices of the SAX stack at different levels (apical, mid-ventricular, basal) and a 4-chamber LAX slice are shown. Mild ghosting and blurring may be visible on some sgs images but all are free from flow- and eddy current-induced dark flow artifacts. SAX: short axis. LAX: long axis Figure 3.8. Comparison of LV functional metrics as measured from ECG BH and sgs FB images. As measured from the SAX stacks, (a) the end-diastolic volume (EDV), (b) end-systolic volume (ESV), (c) ejection fraction (EF), and (d) end-diastolic myocardial volume (EDMV) of the free-breathing self-gated sorted golden step (sgs FB) images show good agreement with those of the ECG-gated breath-hold references (ECG BH), with average absolute errors of approximately 5% or less. LV: left ventricle Figure 3.9. Comparison of LV blood-myocardium sharpness of ECG BH and sgs FB images. For each combination of slice orientation and cardiac phase, the sharpness of the free-breathing self-gated sorted golden step (sgs-fb) images is in general similar though slightly lower than that of the ECG-gated breath-hold (ECG-BH) reference images. SAX: short axis. LAX: long axis. DIA: end-diastole. SYS: end-systole. LV: left ventricle Figure 4.1. T 1 and T 2 relaxations of the magnetic spin. The spin at equilibrium (a), which is aligned with the scanner main field along the z-axis, is tipped into the transverse plane by a 90 RF pulse (b). Over time, the longitudinal magnetization M z(t) recovers while the transverse magnetization M xy(t) decays (c e). The recovery and decay are exponential with time constants of T 1 and T 2, respectively xx

21 Figure 4.2. The T 2 Prep. (a) The schematic of a T 2 Prep with two refocusing RF pulses. (b) The reaction of two spin species: as an example, the longitudinal magnetizations of two spin species are at rest along the z-axis (Time Point 1). After the initial 90 excitation pulse, the magnetizations are in the transverse plane (Time Point 2) starting to undergo T 2 decay at their respective rates. During the decay, the refocusing RF pulses undo any spin dephasing, until desired magnetization difference is attained (Time Point 3). Then the transverse magnetizations are restored back onto the z-axis (Time Point 4), ready for imaging at any flip angle. (c) The T 2 Prep with four refocusing RF pulses, with the key time points labeled Figure 4.3. Cardiac diastolic imaging with the T 2 Prep. Breath holding is not possible due to the total length of such scans. In conventional respiratory motion tracking (a), the pencil-beam navigator (diaphragm navigator) is placed after the T 2 Prep, which delays the subsequent acquisition of a k-space segment, potentially allowing some T 2-weighted contrast to degrade before imaging data collection. If motion tracking can be merged with the T 2 Prep, imaging data acquisition can begin immediately (b). This would allow more T 2-weighted contrast to be captured, or a longer segment to be acquired before the contrast degrades, hence shortening the overall scan duration by some multiples of the R-R interval Figure 4.4. By building motion tracking into the T 2 Prep, imaging data acquisition can begin immediately afterward (a). Fully rewound encoding gradients are inserted into the innermost pair of RF pulses of the T 2 Prep. Each readout acquires a volume projection onto a coordinate axis. To study projections of the moving phantom, 6 readouts are inserted onto one axis (b). For free-breathing human scans, one projection is inserted onto each axis (c) to cover all three axes and to sample as close to the center of the T 2 Prep as possible Figure 4.5. Example images of static phantoms acquired to test the impact of the number and orientation of projections on image quality. One, three, and six projections were inserted into the T 2 Prep along the x, y, and z physical coordinate axes in transversal, sagittal, and coronal imaging slices (all phantom images can be seen in the Results). Only transverse images with xxi

22 projections inserted along the x-axis are shown here (b d), compared against their reference image (a). The relative RSSE of each image with respect to its reference was calculated over the concentric square regions (dashed) around the scanner isocenter, with sides of 12.5, 10, and 7.5 cm Figure 4.6. Static phantom scans acquired to test the impact of number of projections on image quality. In Columns 2 through 4, one, three, and six projections were inserted into the T 2 Prep along x, y, and z physical coordinate axes, and transversal, sagittal, and coronal slices were imaged. Comparing to the reference standard T 2 Prep images (col. 1), only the highest number of x and y projections appear to cause signal degradation in the outer regions, and only along the z coordinate axis (coronal and sagittal slices of col. 4). Otherwise the insertion of projections does not visibly affect image quality Figure 4.7. Relative root-sum-square error (RSSE) of static phantom images with one, three, and six projections inserted into the T 2 Prep along the x, y, and z physical coordinate axes in transversal (tra), sagittal (sag), and coronal (cor) imaging slices. For each image, the relative RSSE error was calculated against the standard T 2 Prep reference over three concentric square regions centered on the scanner isocenter, with sides of 12.5, 10, and 7.5 cm. Using the same method, the baseline or background (Bgd) relative RSSE was also calculated from the three possible pairs of repeated standard T 2 Prep images for each slice (dashed). The error after projection insertion is very low near the isocenter for any number of projections along any axis, at a level similar to the background error. As expected, in any one region, more projections lead to increased error. (tra x: projections inserted along the x axis when imaging the transverse slice. Bgd tra: background relative RSSE of the transverse slice.) Figure 4.8. Motion-tracking projections and final images obtained from a moving phantom. Six projections along the y coordinate axis were inserted into a 40-ms T 2 Prep, filling the entire time gap between the two refocusing pulses. The resultant projections over 90 simulated heartbeats or 72 sec are shown (a f). The total signal magnitude (readout DC-center xxii

23 magnitude summed over time) are comparable across all six projections, with slightly higher values near the center of T 2 Prep due to the expected spin echo refocusing. Motion is clearly revealed on all six projections, and motion can be readily extracted (dashed lines). As compared to the standard T 2 Prep reference (g), the insertion of projections did not visibly disturb the quality of the stationary image (h). The gated image (i) shows the effective removal of motion (j). (6y: six projections were inserted into the T 2 Prep along the y coordinate axis.) Figure 4.9. Projection streams and images of a human subject. Three projections, one along each coordinate axis, were inserted into a 40 ms T 2 Prep. The projections over 90 heartbeats are shown in a c. Respiration is revealed along all axes, and the automatically extracted motion waveform (dashed) is superimposed on each. As compared to the standard T 2 Prep reference (d, e), the inserted projections did not visibly disturb image quality, for both breath hold (f, g) and free breathing (h, i). The gated reconstructions (h, i) show the effective removal of respiratory motion (j, k). (1x1y1z: one projections inserted along each axis in the T 2 Prep; BH: breath hold; FB: free breathing.) Figure Comparison of image quality metrics. Image sharpness was measured from intensity profiles drawn on the left-ventricular blood-myocardium border (a). Comparing to breath-hold standard T 2 Prep scans, the gated free-breathing T 2 Prep scans with projections produced comparable image sharpness in both short-axis (SAX) scans (b) and long-axis (LAX) scans (c). Blood-myocardial contrast-to-noise ratio (CNR) was measured from blood and myocardial regions of interest (ROIs) (d), and normalized by the CNR of the reference scan (Standard T 2 Prep, BH) at the same ROIs. The insertion of motion-tracking projections alone (T 2 Prep 1x1y1z BH) minimally impacted relative CNR, with mean ± standard deviation of 99.5±5.42% for SAX (e) and 96.9±2.73% for LAX (f). Free-breathing scans gated with the projections (T 2 Prep 1x1y1z FB) saw mildly reduced relative CNR: 87.0±10.1% for SAX and xxiii

24 89.8±5.33% for LAX due to the occasional missing k-space data after motion gating. (1x1y1z: one projections inserted in T 2 Prep along each axis; BH: breath hold; FB: free breathing.) 121 Figure T 2-weighted contrast of cardiac lesions on two swine models: lesion induced by radiofrequency ablation applied epicardially on the same day of imaging (a), and reperfused acute myocardial infarction induced by coronary occlusion performed two days prior to imaging (b). Comparing to the standard T 2 Prep (col. 1), the inserted projections (col. 2) did not visibly impact image quality. Respiratory motion tracking was effective, and the gated reconstruction (col. 3) maintained both sharpness and contrast. As references, gadolinium delayed-enhancement inversion recovery scans (col. 4) and black-blood turbo spin echo (TSE) scans (col. 5) were performed to delineate the extent of the lesions. (1x1y1z: one projections inserted in T 2 Prep along each axis; BH: breath hold; FB: free breathing; TSE: turbo spin echo.) xxiv

25 LIST OF TABLES Table 2.1. Extraneous phase accumulation of a flowing spin at position y with velocity along the phase-encode direction V, as a function of how long it has been in the imaging slice. As the rightmost column shows, extraneous phase accumulates over time, and as a function of the velocity (m/s) and 0 th moment of gradients (T/m sec). The accumulated phase is simulated and visualized below. (Note that the 0 th moments of i th TR, M 1, M 2, M i, may all have different signs. Refer to the previous figure for Labels A, B, C, D, E, TA, and TB.) Table 3.1. LV functional metrics measured from ECG BH and sgs FB images. ECG BH: ECGgated breath-hold reference cines. sgs FB: free-breathing self-gated sorted golden step cines. EDV: end-diastolic volume. ESV: end-systolic volume. EF: ejection fraction. EDMV: enddiastolic myocardial volume. LV: left ventricle Table 3.2. LV blood-myocardium sharpness of ECG BH vs. sgs FB images. ECG BH: ECG-gated breath-hold reference cines. sgs FB: free-breathing self-gated sorted golden step cines. SAX: short axis. LAX: long axis. DIA: end-diastole. SYS: end-systole. LV: left ventricle xxv

26 1 INTRODUCTION 1

27 1.1 Magnetic Resonance Imaging Magnetic Resonance Imaging (MRI) is a versatile modality in medical imaging because of its superior soft-tissue contrast, high spatial resolution, ability to image arbitrary plane or volume, and the lack of ionizing radiation. A vast body of work has been developed in the field of MRI, from hardware engineering to signal acquisition to clinical applications. Because the present work is within the realm of signal acquisition techniques, the most relevant topics in MR signal and image formation are briefly reviewed in this section Signal and Contrast Formation MRI, as applied in medicine, is primarily the imaging of hydrogen nuclei. The hydrogen nucleus has nuclear spin. When placed in strong magnetic field, such as B 0, the main magnetic field of the MRI scanner, the axis of the spin aligns with the direction of the main field at an angle of either 54 or 126. Because the 54 alignment is slightly more likely, a volume of hydrogen nuclei (such as a voxel, i.e. a pixel in 3D) collectively exhibit a net magnetization M 0 along the direction of B 0, which is typically designated the z-axis. M 0 can be tipped away from the z-axis by a radiofrequency (RF) excitation pulse circularly polarized about the z-axis at the Larmor Frequency, 0 = B 0, where is the gyromagnetic ratio (radians/second/tesla), a physical constant for a chemical element. M 0 now deviates from the z-axis by an angle of, which is known as the tip angle, and precesses about the z-axis at the Larmor Frequency. It is important to note that, the tipped magnetization, M, now has both a component along the z-axis, M z, and a component in the plane perpendicular to the z-axis, M xy, which is known as the transverse magnetization. As a magnetic moment that rotates about the z-axis at the Larmor Frequency, the transverse magnetization generates an electromagnetic signal measurable by a receiver coil. In fact, the underlying image of interest, (r), where r is the spatial coordinate in 2D or 3D, is typically a complex-valued map of the transverse magnetization, M xy(r), at the time of imaging data collection. 2

28 It is possible to distinguish tissue types or diseased states based on the spatially varying M xy(r). Different tissues in the body tend to have different M 0 s, which will directly yield different M xy(r). Moreover, after the excitation pulse, M xy starts to decay and M z starts to recover, both in an exponential fashion, with time constants, known as T 1 and T 2, respectively. Different tissues have different T 1 and T 2 values. This makes it possible to further manipulate M xy and M z by utilizing the different recovery rates to amplify the differences in tissue M xy s, thus achieving desired contrasts in M xy(r). Utilizing both the tissues innate densities of magnetization as well as the active manipulation of M xy and M z, MRI allows powerful control of tissue contrasts, especially those among the soft tissues, and those between water and fat. More details on contrast manipulation pertaining to the current work are discussed in Chapter Spatial Encoding and the k-space Although (r) can be measured using a receiver coil, such measurement amounts to the gross sum of (r) of the entire excited slice or volume. Spatial localization must be achieved otherwise to recover an image, i.e. (r) as a function of space. In MRI, spatial localization is accomplished by encoding the image via the spatial Fourier transform. In other words, MRI measures the spatially independent Fourier data of (r), and decodes the data to recover a spatially dependent function, (r). This Fourier encoding in physical space is realized by taking advantage of the phasor (complex) nature of (r), and the similarity between linear phase applied using magnetic gradients and the Fourier transform. The discussion below introduces more details on spatial encoding, leading to the concept of k-space. The vector quantity (r) can be expressed as a phasor quantity, i.e. a complex exponential with a magnitude term and a phase term: (r) = A(r)exp[j (r)]. The complex exponential carries the rotational phase of (r) in the xy-plane, and the rotational phase can be controllable by varying the local strength of the magnetic field, according to = B. Relative to a magnetization that 3

29 experiences only the scanner main field B 0, a magnetization that is subject to a superimposed field along the same direction as B 0 will accrue an additional phase (in radians) of: = B T, 1-1 where B is the magnitude of the superimposed field, and T the duration of the superposition. It is possible to make B a linear function of space. For example, in a 1D space where the underlying image of interest is (x), B can be made to linearly vary along the x direction with slope G x (tesla/meter), i.e. B = x G x. Then the phase accrual would also be a function of x: (x) = x G x T, 1-2 where the slope G x is known as the x-gradient and is realized using the scanner s gradient coils. Because the scanner hardware must ramp up the and ramp down the gradient with finite speed, G x is in fact a function of time, G x(t), and the phase accrual becomes: t φ(x, t) = γx G x (τ)dτ With such additional phase, the magnetization at position x and time t would be: t ρ(x) φ(x, t) = ρ(x)exp [ jγx G x (τ)dτ] Measuring this signal using a receiver coil amounts to integration in space (ignoring coil sensitivity), yielding a function of time s(t): t s(t) = ρ(x) φ(x, t) dx = ρ(x)exp [ jγx G x (τ)dτ] dx Suppose we define k x as: k x γ 2π G x(τ)dτ 0 t 1-6 which is Equation 1-3 divided by 2 so that k x has units of cycles/meter. Note that k x is a function of time. Then Equation 1-5 becomes: 4

30 s(k x (t)) = ρ(x)exp[ j2πxk x ] dx, 1-7 which is indeed a spatial Fourier transform that transforms a complex vector in x-domain into a complex vector in the spatial frequency k x-domain. The latter domain is known as the k-space. In other words, the k-space is simply the spatial frequency space. From the perspective of Fourier transform, the complex exponential is the basis function of the linear transform. Each basis function measures the underlying image at a specific spatial frequency. The higher the k x value, the higher the measurement spatial frequency. Data measured at high k x values collectively represents fine details of the image and determines the spatial resolution of the image. Once all measurements are performed, the k-space is considered fully sampled (more details below), and the underlying image (x) is recovered by performing an inverse spatial Fourier transform of the acquired data. The above example is easily generalized to 2D and 3D. In 3D, for example, the underlying image is (x, y, z), and the gradient is now a vector with three components along the three coordinate axes: G(t) = < G x (t), G y (t), G z (t) >, which is realized by three separate sets of gradient hardware in the scanner. B is now a dot product of the position vector and the gradient vector: B = r G(t). The k-space is also a 3D vector: k(t) = < k x (t), k y (t), k z (t) >, where: k x (t) γ 2π G x(τ)dτ 0 t k y (t) γ 2π G y(τ)dτ 0 t 1-8 k z (t) γ 2π G z(τ)dτ Finally, the signal measured from the receiver coils constitutes a 3D Fourier transform: 0 t s(k x (t), k y (t), k z (t)) = ρ(x, y, z)exp[ j2π(xk x + yk y + zk z )] dxdydz, 1-9 which can be written in vector form: 5

31 s(k(t)) = ρ(r)exp[ j2πr k]dr 1-10 The k-space is a useful formalism, first because any particular spatial encoding of the underlying image at a moment in time can be described as a location in the space. Secondly, the realizable vector gradient G(t) is continuous and finite-valued, suggesting any gradient would result in a continuous trajectory in the k-space. As in Equations 1-8, the magnitude of G(t) directly determines the rate of change of k(t). In other words, the k-space allows the intuitive notion that the gradients steer the current position of the spatial encoding in the space, allowing one to design G(t) according to the desired k-space position and velocity The 2D Cartesian k-space in Practice Because the present work focuses on 2D Cartesian imaging, this discussion is restricted to the 2D Cartesian k-space, but is generalizable to 3D Cartesian imaging. Besides Cartesian, the k-space can also be radial, spiral, rosette, etc., which are beyond the scope of this work. In practice, the k-space signal s(k x, k y) as measured by the receiver coils is sampled, digitized and stored in computer memory. In other words, only a finite number of discretely data points in the spatial frequency domain are measured. And because discrete and finite sampling in the frequency domain results in a band-limited and cyclical signal in the image domain [1], the underlying image (x, y) must also be treated as discrete (and cyclical, more details to follow). The discrete 2D Cartesian k-space data can be expressed as s[u, v] = s(u k x, v k y), where k x and k y are the sampling intervals in k-space, and u and v are the sample indices. Similarly, the discrete image can be expressed as [m, n] = (m x, n y), where x and y are the pixel size of the image (known as the in-plane resolution of the image), and m and n are pixel indices. The Fourier transform in Equation 1-9 becomes: 6

32 s[u, v] = ρ[m, n]exp[ j2π(m x u k x + n y v k y )] j i 1-11 Typically, the imaged object is expected to be within some limits of spatial extent, known as the field of view (FOV). The image to be produced therefore has size of FOV x and FOV y, to be composed of N x and N y pixels, respectively. As a result, x = FOV x/n x and y = FOV x/n x. Under this definition, the highest spatial frequency that the image can carry is ½N x/fov x cycles/meter (e.g. one pixel bright, next pixel dark, and so on) along the x-axis and ½N y/fov y cycles/meter along the y-axis. According to Nyquist sampling criterion, to fully sample a signal, the sampling rate must be at least twice the maximal underlying frequency, i.e. 2 ½N x/fov x and 2 ½N y/fov y along the x- and y-axis. In other words, k x and k y must reach N x/fov x and N y/fov y. Because for an orthogonal transform the dimensionalities of the input space and the output space are equal, k x = N x/fov x and k y = N y/fov y are covered in N x and N y equal spatial frequency steps. Therefore, the spatial frequency step sizes are k x = (N x/fov x) / N x = 1/FOV x and k y = (N y/fov y) / N y = 1/FOV y, respectively. In other words, the k-space sampling interval in any dimension is equal to the inverse of the desired spatial FOV in that dimension. (Note that, as a consequence, the lowest spatial frequency measured in any direction is 1 k, meaning that the longest spatial period of the complex exponentials used to measure the image is 1 FOV, the measurements cannot perceive any object with size greater than 1 FOV. In other words, the image is always treated as a cyclical signal with spatial frequency 1 FOV. Should the extent of the imaged object exceed 1 FOV, the excessive portion will result in foldover on the resultant image. Thus it is important to set an FOV greater than the size of the imaged object in any one direction.) Now that x, y, k x, and k y are all determined in terms of physical quantities, the discretely measured signal in Equation 1-11 becomes: s[u, v] = ρ[m, n]exp [ j2π (m FOV x u N x FOV x + n N x N FOV y v N y FOV y )] x N y N y n m

33 = ρ[m, n]exp [ j2π ( mu + nv )] N x N y n m which is the 2D discrete Fourier transform (DFT). After N x N y discrete samples of s[u, v] have been collected, an inverse DFT is performed on s[u, v] to recover the image of N x N y pixels. In practice, the discrete 2D k-space grid is approximately symmetric around k x = 0 and k y = 0 with one more k on the negative side, i.e. k x ranged from k min-x = ( N x/2) k x to k max-x = (N x/2 1) k x and k y ranged from k min-y = ( N y/2) k y to k max-y = (N y/2 1) k y. An example of the discrete 2D k-space is shown in Figure 1.1. Samples collected at grid points near the origin represent low spatial frequency components of the image, whereas those collected in the outer regions represent high-frequency components. As a result, the interior samples determine the intensity level and contrasts of the image, whereas the outer points determine the fine details. As mentioned earlier, any activity in one or more gradient coils defines a trajectory in the k-space, thus the most straightforward way to sample the k-space is to switch on one or more gradients at a constant level, making a constant-velocity, straight-line trajectory in k-space, and sample data points at equal intervals along the path. This path is known as a readout, an example of which is shown in Figure 1.1. The 2D Cartesian k-space grid is acquire this way, one straight line at a time. Mathematically, each readout can be thought of as holding v in Equation 1-12 constant, and collect samples at all discrete values of u. Because each value of u represents a spatial frequency, the direction indexed by u (x-direction in this case) is known as the frequency-encode direction. During the readout, the fixed v-value adds a constant phase to the complex exponential while the spatial frequency is being incremented, therefore the direction indexed by v (y-direction in this case) is known as the phase-encode direction. Normally, N y readouts at equally spaced phase-encode values must be acquired to have the complete k-space data for an image. However, M xy rapidly decays after it is generated by the excitation RF pulse, allowing only one or a few readouts to be acquired. As a result, the excitation- 8

34 readout process must repeat many times to acquire the complete k-space. The time interval between two repetitions is known as the repetition time (TR). In the present work, only one readout is acquired in each TR, although this need not be the case in other imaging techniques. The series of all such repetitions of gradients and RF pulses necessary to complete an imaging study is known as an MR pulse sequence. 9

35 1.2 Cardiac MRI Overview The heart lends itself well to MRI, because by manipulating magnetic spins, MRI can generate superior contrast among blood, myocardium, fat, and diseased myocardial tissues. Cardiac mechanical function and myocardial motion are captured by cardiac cine imaging, which produces a continuous series of images visualizing the entire cardiac cycle in motion. On the other hand, myocardial tissue characterization (e.g. T 2 mapping, perfusion) is typically acquired by contrastprepared diastolic imaging, which produces a single image of the heart s diastole state, carefully timed to when the tissue spins form the desired contrast. This is known as diastolic imaging. Regardless of the acquisition mode, imaging the heart is challenging due to its constant motion, which is a mix of intrinsic cardiac motion and respiratory motion. If unchecked, they cause severe degradation of image quality including blurring, smearing, and ghosting [2 5]. An example of motion artifact in cardiac imaging is shown in Figure 1.2. Motion must be accounted for, and image data acquisition speed must be as fast as possible. If the motion state of the heart is known throughout imaging, then every readout of imaging data can be accepted or rejected according to the motion state (known as motion gating), or corrected for motion effects (motion correction) The bssfp Given the speed requirement, balanced steady-state free precession (bssfp) became the sequence of choice for cardiac MRI [6 12]. First used in imaging in 1986 [13], the sequence features short TRs, so that readouts can be acquired at high temporal frequency. Modern scanners can achieve TRs of 2~3 ms at diagnostic image resolution. For cardiac MRI, the bssfp brings two key benefits. First, rather than spoiling or crushing all transverse magnetization after each readout, the magnetization is rewound by fully balanced gradients by the end of the TR. During imaging, the magnetization is maintained in a steady state. This makes both short TR and strong signal possible, 10

36 because there is no need to wait for the magnetization to recover. Maintaining the steady state magnetization gives bssfp an SNR advantage over other sequences. Second, because bssfp generates T 2/T 1 contrast, the blood-myocardial contrast and contrast-to-noise ratio (CNR) are excellent [14 16]. An example of bssfp cardiac image, as compared to a gradient echo one, is shown in Figure 1.3. Because of these advantages, bssfp was used throughout this work. The disadvantage of bssfp is its high sensitivity to off-resonance and flow, because the magnetization is always recycled and therefore retains all erroneous phase accrual. The steady-state magnetization in the imaging slice or volume may accrue phase in a spatially varying manner depending on the local main field inhomogeneity. If the phase accrual approaches 180 /TR, the steady-state magnetization diminishes to zero [14], forming strips of dark regions in the image known as bandings. Any moving magnetization in the presence of gradients also accumulates extraneous phase (unless the gradient is designed for flow compensation specifically in the direction of flow), which may disrupt the bssfp steady state, causing significant artifact [17 21]. Off-resonance and flow present significant challenge to bssfp in cardiac imaging because of the numerous tissue types in the thoracic and abdominal cavities and the fast flow of blood in the cardiac chambers Real-Time Cardiac Imaging It is possible to acquire a sequence of MR images at a fast-enough frame rate at which cardiac motion can be neglected. In real-time cine imaging, k-space data for the image frame is repeatedly acquired ignoring cardiac and respiratory motion, typically with a per-frame temporal resolution of 30~60ms. To achieve the high acquisition speed, the gradient hardware works at the maximal capacity allowed by the gradient amplitude and slew rate limits, beyond which peripheral neural stimulation [22 24] may occur in the patient. Given the frame rate requirement, there is insufficient time to acquire enough image data to produce high spatial resolution in the image. Typical in-plane spatial resolution is 2~3mm for real-time images, which is sufficient for the measurement of some 11

37 functional metrics of the left ventricle (LV) such as the volume and mass [25 27]. Finer features of the myocardium are not well visualized Segmented Gated Cardiac Imaging The Standard Segmented Gated Cardiac Imaging To achieve higher spatial resolution than real-time imaging, the k-space for each image frame needs to have a greater extent. However, a greater k-space will require more time to acquire, during which significant cardiac motion will occur. This problem is resolved by segmented imaging: the k-space is divided into N seg segments, where each segment consists of N RO readouts. N RO is typically set to 8~12 depending on the TR, so that each segment takes approximately 30 ms to acquire, as this is the typical desired temporal resolution for cardiac imaging. For cine imaging, a segment is acquired repeatedly during a heartbeat for N cp times, where N cp is the number of cardiac phases or frames desired in the cine. In the next heartbeat, acquisition is incremented to the next segment, and so on. Thus all required k-space data will take N seg heartbeats to complete. An illustration of such cine imaging is shown in Figure 1.4. Segmented imaging requires careful calculations to set up. One must ensure that all cardiac phases fit into the patient s R-R interval, i.e., N RO TR N cp RR. For example, assuming patient R-R interval of 800 ms, TR of 3 ms, and 192 readouts per image, N RO=12 would be a good choice, as it results in a cine with temporal resolution of 12 3=36 ms and 800/36 22 frames. This cine would take 16 heartbeats to complete. On a typical clinical MR scanner, one can achieve a spatial resolution of mm 2 ( mm field of view, matrix size) at TR=3 ms, and a high CNR using bssfp. To achieve higher temporal resolution, smaller segments (smaller N RO) can be used. However, due to increased N seg, more heartbeats will be needed to acquire the complete cine. 12

38 For diastolic imaging, where only one image is produced, a single segment is acquired in every heartbeat, in end-diastole, where cardiac motion is minimal. Similarly, N seg heartbeats are needed to acquire all data. Because the acquisition of each segment is synchronized to the cardiac cycle, segmented imaging requires a reference for cardiac motion. This is known as cardiac gating. The electrocardiogram (ECG) commonly serves as this reference, where the R-waves are detected and considered as the cardiac triggers. All needed heartbeats are typically acquired over between 10 to 20 seconds, long enough for respiration to cause motion artifact. The respiratory motion is typically avoided by instructing the patient to suspend breathing. The segmented, ECG-gated, breath-hold cine imaging produces higher spatiotemporal resolution than real-time imaging. Since its early development [28], it has become the standard method for clinical studies and the gold standard against which experimental cardiac MR imaging methods are compared Limitations of ECG Gating and Breath Holding The use of ECG and breath holds comes with complications. The switching magnetic gradients inside the MR bore induce currents in the ECG lead wires, distorting the ECG waveform and making R-waves hard to detect [29, 30]. In rare situations, the induced currents have caused heating and burn [31, 32]. In the patient body, the blood flowing through the scanner main field also induces currents, further corrupting the ECG signal [33, 34]. Even when the ECG performs normally, obtaining a clear ECG signal on the patient body will require additional setup time, and in some patients prove to be difficult due to patient habitus. Breath holding for 10 to 20 seconds may be difficult for some patients, especially those with cardiac or pulmonary diseases. The patient may also be uncooperative or too young to perform breath holding. Even with able and willing patients, breath holding is not always reliable. Only about half of the patients were found to be able to hold a steady diaphragm position [35], and for the rest, the diaphragm position drifted during breath hold, in the neighborhood of 2 to 3 mm [36], 13

39 which can be twice the in-plane voxel size of the scan. Breath holding has also been shown to increase patient heart rate [36], which may cause the loss of imaging data due to the shortened R- R intervals. For even longer scans such as multislice scans and contrast prepared scans, more than one breath hold is required: the scan is paused after each breath hold to allow the patient to breath. However, the reproducibility of breath holds was found to vary from one patient to another [37], which will cause spatial misalignment of imaging data External Respiratory Tracking Given the limitations of breath holding, additional devices have been developed for respiratory motion tracking. Commonly known as the respiratory bellow [38 40], a balloon-like pouch is placed between patient chest wall and strappings on the scanner bed and is pneumatically connected to a transducer that converts the pouch pressure to a respiratory signal. As the patient breathes, the chest wall exerts changing pressure on the respiratory bellow, and its position is thus pneumatically sensed. Although the respiratory bellow is conceptually straightforward, it is important to note that the bellow is a surrogate measure of the chest wall position, which is in itself a surrogate of the true respiratory position of the heart. It has been shown that how the diaphragm position correlates to the heart s respiratory position differ significantly from subject to subject [41, 42] and the correlation can be corrupted by hysteresis [42]. Even assuming perfect correlation between the diaphragm position and the chest wall position, how the latter is measured by the respiratory bellow depends on how the bellow is set up this is true even with repeated setups on the same subject [43], and therefore the measurement will presumably vary widely from patient to patient. Thus the respiratory bellow is too indirect to be an accurate measurement tool. 14

40 1.3 MR-Derived Motion Tracking Given the various challenges of ECG gating, breath holding, and the respiratory bellow, a large number of techniques have been developed to extract motion from MR-measured signal [6, 10, 11, 44 52]. They typically acquire a subset of k-space for motion extraction at a fairly high sampling rate so as to describe the state of motion at an adequate temporal resolution. As a result, they come at various degrees of overhead to imaging because imaging data acquisition is usually disrupted when the motion measurement is acquired. There is a tradeoff between the amount of motion information measured and the imaging efficiency. Some of the most frequently used sources for motion measurement are outlined below to illustrate the tradeoff Center of k-space The k-space center is the simplest and lowest-cost data source of motion. The k-space center can be easily sampled at the highest temporal resolution (i.e. every TR) with essentially no overhead to imaging data acquisition in both Cartesian [9, 10] and radial sequences [11, 45, 53] because the k- space trajectory always starts with the center in every TR. The magnitude of the k-space center is then filtered and considered a waveform that represents motion. However, because the k-space center represents the summation of the entire imaging slice or volume, successful tracking of cardiac motion requires the total blood signal to vary significantly over time according to cardiac rhythm, which may not be the case if the heart s pumping function is impaired [9], or if the heart chambers show out-of-phase contractions that superimpose destructively [53]. Similarly, using the k-space origin to track the more challenging respiratory motion is reliable for only a subset of cases [10, 53]. Thus, the k-space center provides the highest temporal resolution but the poorest spatial discrimination due to the summation. 15

41 1.3.2 The Diaphragm Navigator To provide more precision in motion tracking than the k-space origin, a 1D signal known as the diaphragm navigator or can be used to track respiratory motion [54]: a small column of tissue spanning the lung-liver boundary on the right dome surface of the diaphragm is excited with a 2D RF pulse [55, 56] and its signal is measured. Also known as the pencil-beam navigator, the column exhibits a sharp signal intensity change at the lung-liver interface. A motion-tracking algorithm will use this intensity boundary to determine diaphragm position. The navigator is typically not placed on the heart itself because every RF excitation of the pencil-beam column alters the local signal and will introduce artifacts in the subsequently acquired cardiac images. Although the diaphragm navigator is quite specific in the region it tracks, it is a costly measure temporally. A 2D RF pulse requires tens of milliseconds to execute, during which no other imaging data can be collected. To ensure meaningful acquisition efficiency and scan time, it is only executed infrequently (e.g. with every heartbeat or every other heartbeat), and thus it can only be used to measure the slower respiratory motion. Also because of the interruption to imaging data collection, it is unsuitable for acquiring cardiac cines, especially bssfp cines where reestablishing the steady state after the interruption would take another tens of milliseconds. The diaphragm navigator is widely used for diastolic imaging (e.g. coronary imaging and contrast-prepared cardiac imaging) to track respiratory motion of the diaphragm as an indicator for that of the heart. The patients in these scans are imaged in free breathing because such a scan is usually 3D and takes minutes to complete [57 59]. It is important to note that although the diaphragm navigator can pinpoint the diaphragm position to millimeter precision, this position may not accurately reflect the position of the heart. The lung-liver boundary position is again a surrogate for heart position, and most applications of the navigator assume it has a linear correlation with that of the heart [42, 60]. However, the actual correlation has been found to vary significantly from person to person [41, 42]. 16

42 In summary, the diaphragm navigator provides a 1D signal that indicates the respiratory position only, with a cost of tens of milliseconds, the inability to work with steady-state cine imaging, and subject-dependent correlation with the heart position Low-Resolution Images These techniques reconstruct a separate series of images on a near real-time basis throughout the scan, and determine motion from such images [45, 61, 62]. Because normal imaging data collection already takes full capacity of the scanner, these motion images must be reconstructed from a subset of the imaging data already being collected, and are therefore of lower resolution and quality than diagnostic images. For this reason, these techniques are typically restricted to radial sequences, where every imaging readout crosses the center of k-space. Thus, a small collection of imaging readouts (e.g. 12), as long as their k-space angles are reasonably uniformly spaced, can be used to form a motion image. Because of the low number of readouts per image, higher-frequency k-space data on these readouts must be removed to avoid undersampling artifacts. Thus, the motion images are of low resolution, but adequate for performing 2D motion correction. A complete, new motion image is acquired every tens of readouts, although the readouts of the motion image can be replaced one at a time, on a rolling basis, as each new readout is acquired. The PROPELLER method, a radial-like sequence, reconstructs the low-resolution images from a small number of parallel lowky Cartesian readouts [44, 63], known as a blade. The blades rotate continuously during imaging, much like in radial sequences, in order to capture motion in all orientations. Although the radial sequence lends itself well to cine imaging, the development of radial sequences is more challenging than for Cartesian sequences because the former is vulnerable to gradient delay error that misaligns the readout at the k-space center, and requires scanner-specific gradient calibration or k-space data correction to avoid significant signal loss in images [64, 65]. Image reconstruction is also more challenging in radial sequences because the radially acquired 17

43 readouts present a k-space with nonuniform sampling intervals. Rather than using a simple inverse Fourier transform, k-space gridding [66] or nonuniform Fourier transform [67, 68] is required, both of which are computational intensive and require setting the correct reconstruction parameters. Even when these technical hurdles are overcome, given the relatively low temporal and spatial resolutions of the motion images, typically only respiratory motion can be derived. Thus, although low-resolution image-based techniques provide the richest motion information (in 2D images), they are restricted to respiratory tracking and radial sequences Projections Projection refers to the summation of the imaging slice or volume onto lower dimensions. Given the image formation mechanism of MRI, the 1D projection of the imaging slice or volume turns out to be a remarkably efficient measurement to acquire. A linear readout in k-space that passes through the k-space center at a particular angular orientation, when transformed back to 1D image space, is equivalent to the original image projected onto a line with the same angular orientation in image space. This is known as the projection slice theorem [69] and is illustrated in Figure 1.5. To derive the theorem mathematically, first one can express p(, r), the projection of an image (x, y) at an angle with respect to the +x axis (Figure 1.5), as: p(θ, r) = ρ(x, y) δ(x cos θ + y sin θ r) dxdy, 1-13 y x where δ(x cos θ + y sin θ r) is the 2D Dirac delta function whose ridge runs perpendicular to the line of projection, and r is the position on the line of projection with respect to the origin (x=0, y=0). This expression utilizes the sifting property of the delta function [69], which is useful in isolating the value of a function at a specific location: 18

44 f(a) = f(x) δ(x a) dx x= 1-14 Then the 1D Fourier transform of p(, r), from radial position r domain to radial spatial frequency domain k r (i.e. the radius in k-space, as shown in Figure 1.5) is: FT r {p(θ, r)}(k r ) = ρ(x, y) δ(x cos θ + y sin θ r) e j2πrk r dxdydr r y x 1-15 Changing order of integration: FT r {p(θ, r)}(k r ) = ρ(x, y) δ(x cos θ + y sin θ r) e j2πrk r drdxdy y x r 1-16 Using the sifting property on the innermost integral: FT r {p(θ, r)}(k r ) = ρ(x, y) e j2π(x cos θ+y sin θ)k rdxdy y x 1-17 Since in k-space, k x = k r cos and k y = k r sin, Equation 1-17 can be written as: FT r {p(θ, r)}(k r ) = [ ρ(x, y) e j2π(xk x+yk y ) dxdy] y x k x =k r cos θ, k y =k r sin θ 1-18 The right-hand side is indeed the 2D Fourier transform of (x, y), evaluated at k x = k r cos and k y = k r sin : FT r {p(θ, r)}(k r ) = [FT x,y {ρ(x, y)}(k x, k y )] kx =k r cos θ, k y =k r sin θ 1-19 which is the statement of projection slice theorem, that the 1D Fourier transform of an image s projection at angle is equivalent to a linear path through the 2D Fourier transform of the image, also at angle, described by k x = k r cos and k y = k r sin. The projection slice theorem is useful in that it suggests acquiring a linear readout through the k-space center immediately provides a projected profile of the imaging slice or volume at the same angular orientation, from which motion can be tracked. This readout is no different from an 19

45 imaging readouts and takes only 2~3 ms to acquire. The 1D projection has been used for motion tracking as early as 1990 [6, 70]. At 128 to 256 points over 300 to 400mm FOV, the 1D projection is processed much like the diaphragm navigator, where an algorithm identifies features on the projection and tracks their displacement. However, on the 1D projection, feature tracking may be more difficult as it is a 1D aggregate of the entire imaging slice or volume, with many superimposed and occluded features. Radial sequences appear to the most amenable to projection-based motion tracking because every radial readout passes through k-space center and is in fact a projection, and motion can be measured in every TR at no time cost. However, because in a radial scan, the angular orientation of the readouts is constantly changing, how image features superimpose and occlude one another is different on every projection. Tracking the displacement of any particular feature would be difficult. As a result, radial projections have only been used to track the pulsatile cardiac motion [45] rather than respiratory displacement. Respiratory motion can indeed be tracked using lowresolution images as discussed above, but at very limited spatiotemporal resolution. In Cartesian sequences, it is possible to also acquire motion-tracking projections in every or every other TR [6, 71], and even at a desired angular orientation [72 74]. However, these techniques require inserting an extra readout into the TR. This lengthens the TR, which not only alters the contrast and quality of the imaging data but also reduces imaging efficiency. Additionally, these techniques would require extensive modification of the standard Cartesian-imaging gradients to achieve customized k-space trajectories. This is not practical for the majority of the MRI sequence programmers in the research community because scanner manufacturers normally only provide access to the application programming interface (API) of the standard pre-designed gradients on their systems. A practical compromise that allows easier use of the projection in Cartesian sequences is to simply use an imaging readout without any phase encode. The k y=0 readout is the only Cartesian readout that passes through the center of k-space and represents the projection of the slice onto the 20

46 image space x-axis. During scanning, imaging data acquisition is regularly interrupted, e.g. every 8~12 imaging readouts, so the k y=0 readout can be acquired [49, 75 77]. Due to the interruption, this method is not suitable for Cartesian cine imaging. But at just 2 to 3 ms per execution, the 1D projection strikes a balance between motion tracking specificity and acquisition cost, and can be readily implemented in Cartesian imaging. 21

47 1.4 Thesis Overview Given the practicality of the projection, this work develops and evaluates several novel projectionbased motion-tracking techniques to enhance the projection s power in motion tracking and expand its applications in cardiac MRI. These techniques target Cartesian sequences, which are easily developed and widely available in cardiac imaging. Chapter 2 describes a 2D Cartesian imaging technique, known as pseudo-projection motion tracking, that can extract both cardiac and respiratory motion entirely from normal Cartesian imaging readouts for the reconstruction of cardiac cines without the need for ECG or patient breath hold and yet at no acquisition cost. Chapter 3 describes a variation of the pseudo-projection technique that dramatically reduces the flow- and eddy current-related artifact in the cardiac cines, and expands its application to covering the whole heart. Chapter 4 describes a motion-tracking technique for 2D contrast-prepared diastolic cardiac imaging, in which the motion tracking is incorporated into the T 2 Preparation (T 2 Prep) module and leaves no temporal footprint. The study of each technique involved simulation, sequence development, imaging experiments of phantoms, healthy human volunteers, and/or animal models on clinical MR scanners, the development of motion-extraction algorithms for cine reconstruction, and the quantitative evaluation of the obtained image quality in terms of image sharpness, contrast-noise ratio, cardiac functional measures, etc. 22

48 Figure 1.1. Example 2D Cartesian k-space, a Cartesian readout, and the gradients to realize the readout. (a) shows a simplified discrete 2D Cartesian k-space with only 16 sample points along both k x and k y (N x = N y = 16), centered on (N x/2+1)-th and (N y/2+1)-th sample point from k min-x and k min-y. Superimposed is a single Cartesian readout with N x samples (Segment 2), along with two transitional k-space trajectories (Segments 1, 3) that start and end with the k-space origin as a feature of steady-state imaging. The readout is typically along the k x or frequency-encode direction, whereas k y is known as the phase-encoding direction. Normally, N y readouts at the N y-many equally spaced phase-encode positions are acquired to have the complete k-space data for an image. (b) shows the gradients that realize the entire k-space trajectory, with shaded portions labeled with their corresponding k-space trajectories. Note that the z-gradient is the slice selection gradient along the z-axis, and its k-space trajectory is not visible on a 2D graph of k x and k y. The radiofrequency (RF) excitation pulse is also shown although it does not affect the k-space trajectory. (c) Shows the magnitude of an actual k-space, which corresponds to the imaging slice (d). Because the Fourier transform removes all spatial information from the input signal, any feature in an image is dispersed to all parts of the k-space, and as a result the appearance of the k-space is largely uninformative to the human eyes. 23

49 Figure 1.2. Example of motion in cardiac imaging: An MR image of the cross section of the human heart is seen in (a) where the respiratory motion was avoided by breath holding. When breath holding is unsuccessful or impractical, the respiratory motion causes significant corruption of the image (b). When motion is accounted for by using motion-tracking techniques, which, for example, only accepts imaging data at a single motion state, a clear motion-free image can be obtained despite the presence of breathing motion (c). Figure 1.3. Comparison of balanced steady state free processing (bssfp) (a) and gradient echo (b) cine frames of the same slice at the same spatial resolution on a 1.5 T MR system. The bssfp image of the heart is superior in terms of blood-myocardium contrast and signal-to-noise ratio. Additionally, bssfp imaging is faster due to its short repetition time (TR): in this example, the cine frame rate is 50% higher than that of the gradient echo. These advantages make bssfp the natural choice for cardiac MR imaging. 24

50 Figure 1.4. The acquisition of a segmented ECG-gated cardiac cine. The cine has N CP cardiac phases or image frames (a). Because the k-space for a single image frame cannot be acquired within the desired temporal resolution (~30ms), the k-space is divided into N seg segments (b), each of which can be acquired at such temporal resolution. The i-th segment is acquired repeatedly (for N CP times) during the i-th heartbeat in a scan, guided by an external ECG (d). After N seg heartbeats, the scan is complete with N CP frames of k-space. 25

51 Figure 1.5. The projection slice theorem: in k-space (a), if a linear measurement passing through the k-space center at is made at a particular angular orientation (c) and then inverse Fourier transformed into 1D spatial domain (d), it is the same signal as the original image projected onto a line of the same angle in image domain (b). 26

52 2 PSEUDO-PROJECTION DRIVEN CARDIORESPIRATORY SELF-GATED CARDIAC CINE IMAGING 1 1 Adapted from: L. Guo, J.A. Derbyshire, D.A. Herzka. Pseudo-Projection Driven, Self-Gated Cardiac Cine Imaging Using Cartesian Golden Step Phase Encoding. Magnetic Resonance in Medicine 2016;76(2):

53 2.1 Abstract Whereas most self-gated cardiac MRI techniques can only track either respiratory or cardiac motion and comes with various degrees of overhead to imaging data acquisition, in this work a novel 2D self-gated imaging technique is developed for Cartesian cardiac cine MRI without breath hold or using ECG. It is also free of motion-detection overhead and requires minimal planning for motion tracking, making it the first report of a technique with such capabilities. In this technique, motion along the readout direction was extracted solely from normal Cartesian imaging readouts near central (k y=0) phase encode (PE). During imaging, the readouts below a certain k y threshold were scaled in magnitude and filtered in time to form pseudo-projections, enabling projection-based motion tracking along the readout direction without frequently acquiring the central PE. A discrete golden step PE scheme allowed the k y threshold to be freely set after the scan while maintaining motion sampling that is uniform both in time and in k y. The PE scheme was studied using simulation, and the motion-tracking ability of the pseudo-projections was evaluated using imaging studies of healthy human subjects. The pseudoprojections displayed sufficient spatiotemporal resolution for both cardiac and respiratory tracking, allowing retrospective reconstruction of cardiac cines without breath holding or electrocardiogram (ECG). The resultant images were found to have comparable quality, as measured by sharpness and functional metrics, as standard breath-hold ECG-gated cines, despite having some sensitivity to flow- and eddy current-induced artifact. 28

54 2.2 Introduction As discussed earlier, for a linear readout in k-space to be a projection, it must pass through the center of k-space. This seemingly makes radial sequences a convenient choice because every imaging readout passes through the k-space center. However the constantly changing projection angles makes motion tracking difficult, and even when low resolution image based motion tracking is employed, radial sequences themselves involve technical complications in implementation and image reconstruction. In Cartesian imaging, on the other hand, only one imaging readout passes through the k-space center (k y=0) per k-space acquisition. As a result, to measure motion at a reasonable temporal rate, one must incur the cost of regularly interrupting imaging data acquisition to acquire the k y=0 readout. However, even when a Cartesian imaging readout does not pass through the k-space center, if it is sufficiently near center, it may in fact carry enough information about the imaging slice for motion tracking. Single Cartesian readouts between 4 and 14 Δk s have been used to estimate rigid body displacement in both x- and y-directions [78]. In addition to translational motion, near-center readouts have been used to detect and correct rotational motion [79]. Groups of off-center Cartesian readouts have also been used to estimate 2D rigid body displacement and screen non-rigid motion [80, 81] (although there is not enough information to correct the non-rigid motion). Such reported techniques are all intended for acquiring single-frame static images, and none has been applied to multi-frame cardiac cine imaging. In Cartesian cardiac cine imaging, the k-space is to be acquired continuously and all regions of the k-space are to be acquired with equal preference. Then it is possible in principle to rearrange PE ordering so that the near-center region of the k-space is acquired at a regular rate by the imaging readouts themselves. The near-center readouts would serve the dual purposes of supporting image formation and motion tracking. Under such arrangement, there would be no need to interrupt 29

55 imaging data acquisition and no additional overhead of acquiring motion, much like in radial sequences. In this work the discrete golden step PE scheme is used to attain that ability. Additionally, the golden step brings the benefit that the near center region of k-space can be freely defined after the scan without affecting the uniform motion sampling in both time and k y. The challenge remains in devising and validating such motion extraction for both cardiac motion and respiratory motion. To that end, imaging studies of healthy human subjects are to be carried out using the technique, and the resultant cine image quality is to be compared with that of the standard segmented ECG-gated breath-hold cines in terms of image sharpness and cardiac functional measurements. 30

56 2.3 Theory This section shows mathematically how a 2D object projects onto a stream of near-center Cartesian readouts to reveal its x motion. It also presents the golden step scheme and its key benefits: the uniform coverage of the k y space and the flexible adjustment of motion tracking after the scan Motion Tracking Using Near-Center Cartesian Readouts In this work, the interval centered on k y=0 within which the Cartesian readouts are considered near center and used for motion tracking will be referred to as the navigator zone. For a 2D object f(x,y), the x inverse Fourier transform of the central phase encode is its projection along the x-axis, and can be written as: j2 yky p x f ( x, y)e dy f ( x, y) dy ky Because f(x Δx, y) would yield p(x Δx), translational motion of the object along x is preserved in its projection. Existing motion-tracking algorithms [76, 82, 83] can readily process p(x Δx(t)) to extract the displacement Δx throughout time. In this work, we define the pseudo-projection as the magnitude of the x inverse Fourier transform of a non-central phase encode, which can be written as: j2 yky A( x, ky) f ( x, y)e dy 2-2 Because only magnitude information is taken, any object displacement (assuming rigid motion) along the y-direction is not reflected on its pseudo-projection: y,1 y,1 j2 yk y,1 A'( x, k ) f ( x, y y)e dy j2 yk y,1 j2 yk y,1 f ( x, y)e dy e A( x, k ) 2-3 A key assumption of this work is that the pseudo-projection at a higher k y can be related to the magnitude of the central projection at k y=0 with: 31

57 , y, y, y 0 A x k c x k A x k, 2-4 where the magnitude scaling factor c(x, k y) is dependent on the particular slice imaged, and can be obtained from fully-sampled x-k y domain data. Ideally, a separate magnitude scaling factor c(x, k y) needs to be found for each motion state. Since motion is unknown, the x-variation of c(x, k y) is assumed to be small enough such that a single c(x, k y) can be used for all states of x-motion. For a motion scan, c(x, k y) can be determined from the average of all data acquired, which is the average of all motion states. Thus for any displacement Δx, it is assumed that:, y, y, y 0 A x x k c x k A x x k 2-5 In other words, we can approximate the true central-k y projection of an object using the k y- and x- dependent scaling of a non-central pseudo-projection. Note that the above expression is meaningful only to a limited extend of k y, because as k y grows large, A(x, k y) magnitude eventually diminishes to noise-level and the magnitude scaling factor c(x, k y) becomes unreliable. The limit in k y depends on the size of the image feature being tracked. It is expected that a feature (assuming fairly constant intensity across) of size 1/m field of view (FOV) leaves significant signal footprint on the pseudo-projection up to k y = mδk y. This is because at mδk y, the Fourier complex sinusoid along the y-axis has a spatial period of exactly 1/m FOV. At k y > mδk y, the feature is larger than the sinusoid period, and much of the feature intensity is canceled by the whole periods within its extent. Therefore, smaller features retain stronger intensity even on pseudo-projections of higher k y. This is visualized with simulations later. 32

58 2.3.2 Golden-Step Phase Encoding The Original Radial Golden Ratio The original use of the golden ratio in MRI was an application to 2D radial dynamic imaging [84]: radial readouts were continuously acquired during a scan and their azimuthal angles were spaced at a real-value golden-ratio increment, which is 180 /φ 111.2, where φ is the golden ratio, (1 5) / At this increment, every additional readout acquired fills in the largest angular gap remaining. As a result, regardless of scan length, no two readouts will have the same angle, and the coverage of the angular space will always remain approximately uniform. This allows for an open-ended scan where any additional scan time would contribute data to all regions of the angular space with equal preference. This arrangement can be seen in Figure 2.1. Also, in a temporal window of arbitrary widths positioned at arbitrary positions during the scan, the readouts coverage of the angular space is still approximately uniform, allowing for retrospective slidingwindow reconstruction of image frames at arbitrary temporal resolution. The flexibility of freely choosing temporal resolution after the scan is highly favorable comparing to having to fix temporal resolution and other motion-tracking parameters before the scan (as in segmented ECG-gated cardiac cine scans) The Cartesian Golden Step The golden ratio can be adapted for Cartesian imaging: instead of incrementing in the angular space, here the golden ratio is used for stepping the PE in the k y space, hence golden step. Namely, if the k y space is described as the interval of [0, 1), every PE would be incremented by 1/φ 0.618, and wrap around if 1. More detailed description can be found in a prior report [85]. However, using this approach, the PEs would not fall on a regular k y grid, and image reconstruction could not use Fourier transform but would require the computationally intensive k-space gridding, where image quality may also be affected by the choice of gridding parameters. 33

59 For the sake of studying motion tracking, in this work an integer variation of the Cartesian golden step is used: in a k y grid comprised of F N phase encodes (PEs) indexed 1 to F N, where the first PE position is the most negative k y, the PE position is advanced by F N 1 lines with every readout. F N 1 and F N two are consecutive Fibonacci numbers (e.g., F N 1=89, F N=144), at the golden ratio of 1/φ The PE position is wrapped around if it exceeds F N, i.e. the nth acquired PE is at position (n F N 1) mod F N. As a result, all PEs in k-space are acquired exactly once every F N readouts 2. This PE arrangement can be seen in Figure 2.2a. The key features of the golden ratio are preserved for Cartesian imaging in the present work. First, every additional readout acquired also fills in the largest gap remaining in the k y space (Figure 2.2b). Similar to the coverage of the angular space, the PE coverage of the k y space will also be approximately uniform in a temporal window of any duration placed at any position during the scan. As a corollary, because each cardiac phase in cine imaging is in itself a small temporal window, the cardiac phase can be set to an arbitrary width with the assurance that all regions of the k y space for a cardiac phase will be filled with equal likelihood. This allows the number of cardiac phases to be set retrospectively, avoiding the need for calculating the feasible values of cardiac phase number and segment size with the constraint of patient heart rate in segmented ECG-gated imaging. As in a golden ratio radial scan, in a Cartesian golden-step scan, one would simply continuously and repeatedly cover the k-space for an adequate number of repetitions to accumulate enough data. The scan could be terminated at any time without losing uniformity in k y coverage. More importantly for the present work, the golden step also brings great flexibility to pseudo-projection motion tracking. As shown in Figure 2.3a c, regardless of the navigator zone width, readouts fall inside it at approximately constant intervals, and cover the k y subspace within the navigator zone pseudo-randomly and nearly uniformly. Thus, the navigator zone width can be 2 In fact, the number of readouts does not need to be a Fibonacci number. See Discussion section for a simple adaptation that can be used for non-fibonacci k y grid size. 34

60 freely adjusted to attain desired motion-tracking temporal resolution while maintaining the nearuniform coverage of the navigator zone. If 1/q of the full extent of k y is used as the navigator zone, the average temporal interval between two consecutively acquired motion-tracking readouts is then q TRs. To illustrate the importance of the pseudo-randomness of the golden step, another widely used PE ordering, the interleaved ordering, would not be able to provide approximately uniform temporal resolution in the coverage of the navigator zone, because large temporal gaps might exist depending on navigator-zone widths, as shown in Figure 2.3d, e. 35

61 2.4 Methods Simulation To visualize object motion as seen on pseudo-projections, several moving circular phantoms were simulated using MATLAB (MathWorks, Natick, Massachusetts) and their pseudo-projections at various phase-encode positions were generated. Specifically, in discrete-time simulations, phantoms with diameters of 1/2, 1/4, 1/8, and 1/16 FOV, representing solid objects of increasing sizes, were displaced around the center of the FOV along the x-axis (see Results for visualization). The 2D Fourier transform was computed for each frame and the rows at 0, 1, 2, 4, 8, and 16 Δk y were recorded as pseudo-projections Sequence A Cartesian balanced steady state free precession (bssfp) sequence was implemented to carry out discrete golden-step phase encoding. Gradient waveforms were designed using hardware optimized trapezoids (HOT) [86], which minimized the k-space transition times between slice selection and readouts and vice versa: for any user-defined slice orientation, gradients were customized so that during the transitions at least one gradient axis reached the limit of amplitude or slew rate Imaging Experiments With local Institutional Review Board approval and after obtaining informed consent, 8 normal subjects (3 males, average age 29±6 years) were imaged using a 1.5T clinical system (Avanto, Siemens Medical Solutions, Erlangen, Germany). The standard chest phased array and spine coils were used to provide a total of 5 channels, and data was saved separately for each channel. All scans were initiated with a half-flip angle, half-tr opening sequence [87] followed by 100 dummy TRs to transition into steady state. All scans were acquired with a matrix size of (F 12) and 36

62 a mm 2 FOV, resulting in mm 2 in-plane resolution. Other imaging parameters included 10 mm slice thickness, 45 flip angle, and 650 Hz/pixel bandwidth. With the optimized gradients, TR ranged from 2.5 to 2.7 ms in all scans, and TE was TR/2. For each subject, a mid-ventricular short axis (SAX) slice and a 4-chamber long axis (LAX) slice were imaged. For each slice, three scans were carried out. First, a breath-held prospectively ECG-gated segmented cine (ECG BH) was acquired as the gold standard for image quality. Each segment consisted of 12 readouts, resulting in temporal resolutions of 30~33 ms (without view sharing) and 12-heartbeat breath holds. The segments were acquired sequentially from negative to positive k y. Then, the same 144 phase-encode positions were covered using discrete golden step, continuously and repeatedly without ECG gating over a 12-second breath hold to assess cardiac motion tracking alone (GS BH). To assess respiratory motion tracking, a free-breathing goldenstep scan (GS FB) was acquired for 90 seconds, representing approximately 240 complete acquisitions of k-space. The ECG-derived cardiac triggers were recorded during both golden-step scans as the timing reference Post-Processing A schematic of the steps required for processing is shown in Figure 2.4. First, a stream of pseudoprojections from within the navigator zone was formed. Cardiac motion and respiratory motion were extracted independently from the stream and were used to guide the cardiorespiratory binning of imaging readouts. The inclusion of readouts within each bin was further refined using a similarity metric based on the corresponding pseudo-projections for the readouts. Note that cardiorespiratory binning assumed motion periodicity and repeatability, but the subsequent similarity-based selection did not and was designed to help improve accuracy by rejecting dissimilar data. 37

63 Cardiac self-gating was applied to both GS BH and GS FB scans, whereas respiratory selfgating tracking was applied only to the latter. Their image quality was quantitatively compared to that of the ECG BH scans Pseudo-Projection Stream Formation Imaging readouts within the navigator zone were concatenated in time to form the stream of pseudo-projections. Wider navigator zones included more imaging readouts for motion tracking, resulting in a higher sampling rate of motion. However, the additional pseudo-projections from higher k y had lower signal level. In this work, 10% of k y space centered around k y=0 was chosen, because 1/q=10% provided an empirical balance of a motion-measurement interval of 10 TR (equivalent to ~38 Hz) and a tolerable pseudo-projection signal drop-off (to about 20±5% of the signal magnitude at k y=0 across all subjects). The stream of pseudo-projections exhibited significant k y-dependent intensity fluctuation over time, which was normalized using the scaling factor c(x, k y). The scaling factor for each coil, sized F N N x, was found by averaging all acquired navigator-zone readouts at each k y, taking the inverse Fourier transform along readout, and normalizing the resultant magnitude with that of k y=0: c(x, k y ) = s i,k y (x) i M s i,ky =0(x) i M 2-6 where s i,ky is the readout at k y during the i-th repetition of k-space coverage, and M is the total number of repetitions in the scan. Motion was disregarded during the averaging process and one c(x, k y) was used for all motion states. To further reduce k y-dependent intensity fluctuation in the pseudo-projections, the stream was smoothed along time dimension with a Gaussian window, whose full width at half maximum was F N/q points. The aim of the smoothing step was to reduce the risk of any residual intensity fluctuation being detected as a significant motion component. 38

64 Cardiac Motion Tracking The goal of this step was to extract from the pseudo-projection stream a 1D waveform in time that would describe the motion of the heart, from which cardiac triggers would be derived to replace the ECG. First, a simple method based on principal component analysis (PCA) was used to extract the cardiac waveform [47]: the five largest eigenvalues and their corresponding eigenvectors were computed for the pseudo-projections covariance matrix AA T. The matrix A of size N TR (N x N c) consisted of N TR pseudo-projections acquired throughout the scan (N x pixels per projection, N c coils concatenated along the column dimension). The five eigenvectors were each Fourier-transformed in time, and the strongest frequency on any eigenvector between 40 and 90 beats per minute was detected as the cardiac frequency. The latter value was used since it corresponded well with the heart rates of normal subjects, though higher values could also be used for patients with faster cardiac rhythm. The eigenvector with the most energy at this frequency was used as the cardiac waveform. Subsequently, the waveform was filtered by a band-pass filter (lower and upper cutoff frequencies at ½ and 2 that of the detected cardiac frequency) before being passed to a movingaverage-crossing (MAC) algorithm [88], with a moving average window width twice the mean duration of detected cardiac cycles. For each waveform cycle, the algorithm generated four events: peak, trough, up crossing, and down crossing. For each scan, the event type with the lowest variance in event intervals was selected to provide cardiac triggers, although any event type could be used. To quantitatively evaluate the accuracy of cardiac self-gating, the timing error of selfgating events with respect to the ECG-derived triggers was calculated for each type of event: 1) the timing lag of every self-gating event with respect to its corresponding ECG trigger was found. 2) The standard deviation of all time lags was calculated and considered the timing error for the scan. This was repeated for all event types and all golden-step scans. The mean of time lags was not used 39

65 because the cardiac waveform, an eigenvector, might have arbitrary phase lag with respect to signal intensity or anatomical motion. Also as a result, the cine frames were shifted after reconstruction to match the start point of the reference cine. The intervals between pairs of consecutive events were divided into N cp-many cardiac phases using a model that scales systolic and diastolic phases separately according to cardiac cycle lengths [89]. For each golden step scan, N cp was chosen such that the resultant average temporal resolution matched that of its reference scan. Cardiac cycles whose length differed from the mean of the scan by more than 30% were considered irregular and were discarded Respiratory Motion Tracking Respiratory waveform extraction and filtering was similar to that described in the previous section, though with a frequency selection range of 4 to 30 cycles per minute. For respiratory gating, the most frequently occurring value of the respiratory waveform was first identified (presumably at end-expiration, where respiratory motion dwells the longest [90]). A window was then chosen around this value (symmetrically if possible) so that 30% of the time the waveform coursed within this window. Imaging readouts acquired when the waveform was within window were used in the next stage of processing. Given the single respiratory bin, readouts were assigned to N cp-many cardiorespiratory bins, resulting in a cine with N cp frames reconstructed phases Similarity-Based Data Sorting To reduce potential errors due to the periodicity-repeatability assumption in gating, readouts admitted to each bin were further selected for consistency: 1) for each cardiorespiratory bin, the mean of all admitted pseudo-projections was found and regarded as the template pseudo-projection for that bin. 2) Readouts admitted to the bin were ranked by their corresponding pseudoprojections similarity to the template in the sum-square-difference sense. 3) For each k y position in the bin, only the most similar readout (or top two most similar readouts in free-breathing scans 40

66 with abundant data) was used in image reconstruction. If no readout was available at a particular phase k y position in a cardiorespiratory bin, cardiac gating was relaxed to include readouts from the two adjacent cardiac phases, after which the same template-based selection was applied. To enable such similarity-based matching, every readout needed a corresponding projection in the pseudo-projection stream. The stream had a temporal resolution of qtr and was thus linearly interpolated in time to a temporal resolution of 1TR. The final selection of readouts was reconstructed separately for each coil using inverse Fourier transform and combined via root-sum-squares. Parallel imaging or iterative reconstruction techniques were not used as they might affect image quality and confound the results of motion tracking Image Quality Evaluation To measure image sharpness, three profiles were manually drawn across the left-ventricular (LV) blood-myocardium boundary (Figure 2.5a,b). They were drawn on the septal wall to avoid the papillary muscles and trabeculae carnae. Along each profile, the distance (in fractional pixels) it took for the image intensity to rise from 20% to 80% of profile dynamic range was found, and the inverse of the average of the three distances was used as the sharpness [11, 61]. Both SAX and LAX images at end systole and end diastole were evaluated. In addition, as a surrogate for cardiac function, endocardial and epicardial contours were manually drawn on both end-diastolic and end-systolic frames of SAX cines (Figure 2.5c). The area difference (epi minus endo) measured single-slice myocardial area (mm 2 ). The percent area change of the endocardial contour was considered the single-slice ejection fraction. These functional measures of the GS BH and GS FB scans were separately compared with ECG BH, using two-tail paired Student s t-test with modified Bonferroni correction. The threshold of significance level was set at a corrected P-value of

67 2.5 Results Simulation As seen in Figure 2.6, circular phantoms of diameters of 1/2, 1/4, 1/8, and 1/16 FOV retained projection appearance on pseudo-projections at up to 2, 4, 8, and 16 Δk y, respectively. In other words, the phantom s projection image started to vanish when the spatial period of the phaseencoding complex sinusoid approached the phantom size. Smaller objects remained visible when using higher order phase encodes not surprisingly because the signals of smaller objects are more spread out in k-space but with the cost of diminished signal level as mentioned in Theory Pseudo-Projection Formation Pseudo-projection appearance at each stage of processing is shown in an example in Figure 2.7. The pseudo-projection streams generated with various navigator zone widths are compared in Figure 2.8, using data from an example scan. Initially, increasing navigator zone width would reveal more features of motion, but at approximately central 10% of k y, both cardiac and respiratory motions were fully revealed. Beyond 10%, no additional information was revealed and cardiac motion was often suppressed Cardiac and Respiratory Motion Tracking For all subjects imaged, cardiac motion and respiratory motion were captured within the first five most significant eigenvectors of the pseudo-projections covariance matrix. As shown in Figure 2.9, the identified cardiac and respiratory eigenvectors were filtered to form the motion waveform. The correspondence between the cardiac events generated by self-gating and the reference ECG triggers was high Figure 2.9c. As shown in Figure 2.9d, the generated respiratory motion curve closely followed the respiratory motion, including the non-periodic deviations of the motion, as seen in the 42

68 initial portion of the scan. Figure 2.10 shows the quantitative comparison between cardiac motion tracking and reference ECG, aggregated for all imaged subjects except one where ECG data failed to record. Overall, the self-gating cardiac events were accurate to about 30 ms with respect to ECG, with the Trough being the most accurate event type Self-Gated Cine Quality Motion tracking was successful in all golden-step scans. Cines were composed of 25 to 30 cardiac phases to match the temporal resolutions of their respective reference scans. A comparison of ECG BH, GS BH, and GS FB reconstructions is shown in Figure Both golden-step self-gated cines showed very similar image quality as the reference scans. Small features such as the papillary muscles and trabeculae carnae are clearly visualized, and nuances of motion such as the atrial kick can be seen in the motion profiles. However, the golden step cines, especially in LAX cines, were prone to signal inhomogeneity or loss in the regions of rapid blood flow (see Discussion). This is better visualized in Figure 2.12, which compares the entire cardiac cycle. LV myocardial sharpness measurements of the golden-step self-gated cines are compared to those of the reference cines in Figure In general, the self-gated cine sharpness was similar to the references, with SAX sharpness slightly greater than LAX, and end-systole sharpness comparable to end-diastole. As seen in Figure 2.14, the LV blood pool area, the LV myocardial area, and the singleslice ejection fraction as measured on the self-gating cines showed good agreement with those of the reference cines. For each functional metric, no statistically significant difference was found between the self-gated cines and the reference cines at a significance level of Bonferroni-corrected P-value of

69 2.6 Discussion and Conclusion In this work, we have demonstrated the efficacy of using pseudo-projections in cardiorespiratory motion tracking. By deriving both cardiac and respiratory motions solely from imaging readouts, this technique allows for ECG-free and free-breathing scanning without the loss of imaging efficiency typical in other techniques. The quality of the self-gated cardiac cines was similar to the ECG-gated breath-hold cines, making it possible to perform ECG-free and free-breathing cardiac function studies. The foremost advantage of the proposed technique is that it captures both kinds of motion with minimal pre-scan planning, since the optimal navigator zone width can be determined after imaging. The number of cardiac phases (consequently, temporal resolution) can also be adjusted retrospectively, while the k-space coverage in each phase remains uniform. There is no need to fix the number of readouts per segment as in segmented ECG-gated scans. The only remaining motionrelated parameter to be chosen is the total scan duration per slice, which can be set to arbitrary values, with the assurance that any additional scan time will benefit all k-space regions of all cardiac phases equally. This makes the scan duration simply dependent on the scanner time available for each slice Technical Considerations Pseudo-randomness The pseudo-randomness of the golden step is essential for the coverage of the navigator zone. Because the k y of each readout heavily influence how an object would appear on the pseudoprojection, the different influences of different k y values must be scattered over time in an unstructured way, so that they do not affect the object appearance in a time-dependent manner. This is well illustrated in Figure 2.15, where the pseudo-randomness of golden step produces a 44

70 consistent, clear depiction of motion. In comparison, the interleaved PE ordering, which also covers the navigator zone with the same likelihood but in a more structured way, produces time-dependent variation in motion appearance, which would make motion difficult to detect. It is noteworthy that another PE scheme appear to be able achieve similar PE patterns as the golden step: if N PE (the number of PEs on the k y grid) and the jump size are mutually prime (i.e. their greatest common divisor is 1), then the navigator zone can be covered at a regular interval. This is potentially more flexible than the golden step because N PE can be non-fibonacci numbers. However, not all mutually prime N PE and jump size produce such coverage. As shown in Figure 2.16, while some mutually prime pairs appear to produce uniform coverage of the navigator zone, other pairs result in sequential coverage. Having to avoid specific jump sizes would add the burden of pre-scan planning. Even when the coverage appears to be uniform, it lacks pseudo-randomness and in fact shows clear structures (Figure 2.16 Columns 1 and 3) Non-Fibonacci Grid Size Although a Fibonacci number was used as the number of phase encodes (N PE) in this work, N PE need not be a Fibonacci number. For any desired number of phase encode steps, the next greater Fibonacci number can be used to form the k y grid, and the jump size is the next smaller Fibonacci number. During a scan, and any generated indices that are greater than the desired N PE are simply be skipped. For example, if N PE=256, a k k y grid of F 14=377 phase encodes is designed. Any indices greater than 256 is skipped in the actual execution of the readouts. With this approach, coverage of k y is still be pseudorandom, because, just like the navigator zone, the N PE k y-space is simply a subsection of the Fibonacci k y-space. Several examples can be seen in Figure 2.17, where it is clear that the pseudo-randomness is preserved Pseudo-Projection Formation In this work the central ±5% of k y was chosen as the navigator zone width. This choice was an empirical compromise between motion-measurement interval and noise amplification. A wider 45

71 navigator zone can include more readouts and therefore more frequently measures motion, although it is including more higher-k y readouts, which have less signal magnitude relative to noise. The magnitude correction step of pseudo-projection formation, when applied to higher-k y readouts, would amplify such noise. The central ±5% of k y resulted in a motion-sampling interval of 10 TR (~38 Hz), and at ±5% k y, the readout signal magnitude would typically drop to 20% of that of the central (k y=0) readout, as shown in Figure Limitations Motion Detection Pseudo-projections do have the limitation of only detecting motion along the readout direction. For motion tracking to function, a significant component of the motion must project onto the readout direction. However, cardiac cycles can be readily detected regardless of the readout orientation due to the contractile nature of the ventricular motion and the high signal intensity of blood. Also, because the standard SAX and LAX slice orientations are both double oblique, the readout direction in all likelihood will be able to catch a significant component of the respiratory motion, which is predominantly along the superior-inferior direction [60]. As with projection-based techniques, pseudo-projections enable the gating of motion but do not provide enough information for cardiorespiratory motion to be corrected. In theory, rigid body translational displacement along the PE direction can be detected using the phase of nearcenter Cartesian readouts [78]. However, such technique requires phase unwrapping, which limits its accuracy and is sensitive to noise. It also assumes rigid body motion and thus is unsuitable for respiration motion. The pseudo-projections, as they are defined in this work, are magnitude signals and are insensitive to rigid body translational motion and may be corrupted by non-rigid motion. Through-plane motion can be detected only if it produces enough intensity change in the imaging 46

72 plane to project onto the readout direction, and still the displacement of such motion cannot be detected. These limitations would make it difficult to accurately detect respiratory motion, which is more complex and subject-dependent and has motivated many sophisticated subject-specific models (e.g. 3D translational [91], elliptical [92], affine [93], non-rigid [48, 62]). Even with similarity-based data sorting, projection-based gating in the current technique still assumes repeatability of respiratory motion, and one can expect more subject-dependent variability in the performance of respiratory motion tracking Dark Flow Artifact As noted in Results, golden step cines are sensitive to signal inhomogeneity or loss in the blood pool. The resultant artifact, sometimes referred to as the dark flow artifact, has a distinct appearance and is well known in bssfp imaging. It has been attributed to a combination of flow and field inhomogeneity [17, 19 21], both of which disturb the bssfp steady state by introducing extraneous phase to the spins in every TR. The affected spins may lose steady state and undergo oscillation, causing signal inhomogeneity or loss. The large PE jumps between consecutive readouts of the golden step exacerbate the extraneous phase accumulation due to flow. Thus, imaging slices with sustained in-plane flow, such as LAX slices, are particularly vulnerable to the artifact. To qualitatively describe this PE-flow interaction, a bssfp scan model is used (Figure 2.19). In this model, only PE gradients and flow along the PE direction (equivalent to the y-direction for this discussion) is considered, because the acquisition of data points along the PE direction is spread out over a longer period of time than along the readout direction. Significant displacement of a spin due to flow can occur between the acquisition of two neighboring data points along the PE direction, and this gives the characteristic smearing effects of the dark flow artifact along the PE direction only. In an ideal scenario without flow, a spin s phase at the echo time of the i-th TR 47

73 is γym i, where γ is the gyromagnetic ratio, y the y-position of the spin, and M i the 0 th moment of the PE gradient of the i-th TR (the rewinder PE gradient has a 0 th moment of M i). Further, its phase at refocusing points between every two consecutive TRs should be 0. However, with a constant flow, V, the spin s phase at these time points are significantly altered, as shown mathematically in Table 2.1. Combining the series shown in the table, the total spin phase due to PE gradients and flow (disregarding other imperfections such as field inhomogeneity), up to the end of the i-th TR, can be expressed as: i 1 exp ( jγ [ T A V M k + (y + (i 1)V(T A + T B ))M i ]) 2-7 k where γ is the gyromagnetic ratio, T A the time interval between the PE and the rewinding gradients within a TR, and T B the time interval between the rewinding gradient of a TR and the PE gradient of the next TR. Removing the term involving y, which is the intended phase of phase encoding, the extraneous phase is: i 1 exp ( jγv [ T A M k + (i 1)(T A + T B )M i ]) 2-8 k=1 where it is noteworthy that the extraneous phase would accumulate as long as the spin remains within the imaging slice. However, the extraneous phase accumulation may in fact be phase oscillation depending on the signs of M i. The extraneous phase per unit speed is simulated for a spin traveling at a constant velocity along the PE direction for several PE schemes. As shown in Figure 2.20, it is clear that the golden step PE scheme induces more extraneous phase than the linear scheme. For example, a blood spin traveling at 10 cm/sec along the PE direction would experience continuous phase disturbances as much as 1.5 radians per TR by the first 100 ms after it enters the imaging slice. This disturbance will severely disrupt the spin s normal transition to steady state, and the large phase error from TR to TR is the most likely explanation of the characteristic PE-direction smearing of 48

74 the artifact. In comparison, the phase error under linear scheme is a few percent of that of the golden step. The interleaved scheme, which has large PE jumps, also induces significant extraneous phase. This is likely to explain the fact that similar smearing artifact can often be observed on the interleaved scans in addition to golden step scans. Besides flow-induced phase error, the large PE jumps are also known to cause additional phase disturbances by inducing eddy currents in the scanner body [94]. While the extraneous phase due to flow cannot be avoided, measures can be taken to minimize the eddy current effects. At imaging time, PE pairing [94], doubling [95], and other gradient modifications [96, 97] can be used to reduce the eddy current itself. At post-processing time, the dark flow artifact can also be reduced using principles of parallel imaging [98]. Careful shimming of the scanner main field and shifting the center frequency are most likely to improve image quality [17, 19, 21, 99]. Because both eddy currents and imperfect main field can result in unwanted spin phase, improving the local main field will reduce the total extraneous phase accrual and may prevent some spins from undergoing oscillation. At the sequence level, specialized techniques such as S5FP [100] can be used to eliminate spins corrupted by phase and flow. As a last resort, steady-state incoherent techniques such as spoiled gradient echo imaging (SPGR) are much less sensitive to extraneous phase, and can be used to avoid the artifact altogether, especially at higher field strengths, albeit with a very different image contrast and reduced SNR Extensions and Future Work Parallel imaging and compressed sensing were not used in this work, so that motion tracking could be evaluated in isolation. Hence, scan durations in this work were longer than necessary in a clinical setting. Parallel imaging and sparse-recovery reconstruction techniques can be readily applied. For example, given the large amount of data acquired in the golden step scans, it would be straightforward to measure convolution weights for GRAPPA [101] and to achieve acceleration rates of 2 49

75 or 3. Free-breathing scan time could be reduced to approximately 30 sec per slice at 30 ms cine temporal resolution. One can also randomly skip readouts outside the navigator zone and recover them using GRAPPA, calibrated using the fully sampled navigator zone (which in this case must be fixed before the scan). Although this work used integer golden step, the real-valued golden step could also be used in Cartesian imaging [85]: a normalized k y-space is described by a continuous interval of 0.5 to 0.5, and the real-valued PE position therein is incremented by the golden ratio conjugate, Δk=( 5 1)/ , after every readout (and circularly wrapped within the interval). In the realvalued scheme, no PE position is ever repeated, and as a result no limitation exists in the PE matrix size. In other words, there is no need to even set the PE resolution before the scan, because the longer the scan time, the higher the resolution can be upon image reconstruction. However, since the PE position no longer falls onto the Cartesian grid, the magnitude scaling factor c(x, k y) would need to be made continuous along k y, which can be achieved by data fitting or interpolation. Additionally, image reconstruction with real-valued PEs would require k-space regridding or a generalized inversion approach, which may be more computationally intensive and impact image quality in technique-dependent ways, but which may be more amenable to incorporation of sparse reconstruction techniques. The discrete integer golden step used in this work could take advantage of the fast Fourier transform for straightforward image reconstruction and has adequately demonstrated the motion tracking ability of near-center PEs. The pseudo-projection technique can be easily expanded to 3D Cartesian imaging: in the 3D Cartesian k-space, the arrangement of k y and k z would be pseudo-randomly governed by using the multidimensional golden means [102]. Similar to using a central segment of k y, a central rectangle of the k yk z-space can be set as the navigator zone, which will be approximately uniformly covered by readouts. A 2D magnitude correction factor c(x, k y, k z) is derived over this region from data over the entire scan. Note that although navigator zone is now 2D, the resultant pseudoprojection is still a 1D signal, and therefore motion tracking will still be restricted to in 1D. 50

76 2.6.4 Conclusion The use of pseudo-projections in conjunction with golden-step phase encoding has been found to be capable of tracking both cardiac motion and respiratory motions at no cost to data acquisition, and has been shown to be effective for free-breathing, non-ecg cardiac cine imaging, which produced cine image quality comparable to that of breath-hold ECG-gated scans. The greatest benefit of using the golden step for PE ordering is that motion is regularly measured regardless of the k y grid size, the navigator zone width, or the total scan length. All regions of k-space of all cardiac phases are equally likely to benefit from any additional scan time. In other words, there is no need for pre-scan calculation of motion-related parameters (such as the number of cardiac phases and segment size) in the constraints of scan length, heart rate, and k y grid size. One can simply start the scan, use all time available to collect data, and determine the motion parameters later at the reconstruction time. As with any PE scheme with large jumps between two readouts, the golden step does come with some sensitivity to flow and eddy currents. However, the resultant image artifact can be mitigated by main field shimming and choosing slice orientations to avoid bssfp bands and fast PE-direction flow. Because the unique pseudo-randomness of the golden step affords the significant scan-time simplicity that other schemes (e.g. interleaved and mutually prime) cannot provide in all circumstances, it makes the proposed pseudo-projection technique a valuable tool for self-gated cardiac cine imaging. 51

77 ky Gap Size PE Figure 2.1. The original use of the golden ratio in radial dynamic MRI. Comparing to conventional angular increments of the radial readouts (a), which covers the angular space sequentially and starts to repeat angles after the first complete rotation, the golden ratio (b) covers the angular space pseudo-randomly. Every additional readout acquired fills in the largest angular gap remaining. Thus the angular space is covered approximately uniformly, and without repetition regardless of number of readouts acquired IEEE. Reprinted, with permission, from Winkelmann et al, An Optimal Radial Profile Order Based on the Golden Ratio for Time Resolved MRI, IEEE Transactions on Medical Imaging, Jan a Sequential Golden Step Interleaved 72 b Nth TR Figure 2.2. PE execution order of the golden step scheme, as compared to the sequential and interleaved schemes (a). In the golden step scheme, the Cartesian k y grid with 144 evenly spaced PEs and is covered exactly once by incrementing the PE index by 89 for 144 times. In the interleaved scheme, each segment consists of 8 readouts. The size of the largest gap remaining on the k y grid as a function of acquisition time is plotted (b). The golden step covers the remaining gaps the most quickly among the three schemes, as indicated by its steep drop-off near the start of the scan. 52

78 Figure 2.3. The integer golden-step PE ordering (a c): a Cartesian k y grid with 144 evenly spaced PEs is covered exactly once by incrementing the PE index by 89 with each readout, where 89 and 144 are consecutive Fibonacci numbers. A central subsection of k y is used as the navigator zone (dashed lines), within which the imaging readouts are also to be used for motion tracking. The golden-step PE ordering allows for approximately uniform coverage in time and in k y at any navigator zone width, shown here varying from 5% to 15% in a) through (c). In comparison, another commonly used PE ordering, the interleaved ordering (d f), cannot maintain uniformity since it shows large gaps in coverage in certain navigator-zone widths, as in (d) and (e). (An interleaved acquisition of 144 total PEs and 8 readouts per segment is shown here.) pseudo -projections pseudoprojection stream formation stream stream stream cardiac motion tracking resp. motion tracking gates gates similarity -based k-data sorting k-data IFFT cine frames cine Figure 2.4. Overview of the post-processing chain used in this work to derive motion from pseudoprojections and guide cine reconstruction. 53

79 Figure 2.5. Intensity profiles drawn to evaluate the blood-myocardium sharpness (a, b) and contours drawn to evaluate cardiac function (c). Figure 2.6. Pseudo-projection of 2D solid circular phantoms (a) with diameters of 1/2, 1/4, 1/8, and 1/16 FOV were simulated to undergo sinusoidal motion (b). Their x inverse Fourier transforms of readouts at 0, 1, 2, 4, 8, and 16 Δk y phase encodes were generated (c). Smaller phantoms were found to retain projection appearance until higher phase encodes than did larger phantoms, because the Fourier transform of narrower objects are more spread-out in k-space. 54

80 Figure 2.7. Formation of the pseudo-projection stream used for cardiorespiratory motion tracking. One complete coverage of the 144-PE Cartesian k-space (over ~ 375 ms) were acquired using the discrete golden-step phase encode ordering (a). Imaging readouts inside the navigator zone (central 10% of k y) were used for motion tracking, and the magnitude of their inverse Fourier transform, the pseudo-projections, are shown in (b). Imaging data acquisition covered the k-space repeatedly for the entire duration of the scan. The first 1000 raw pseudo-projections (over approx. 28 sec.) are shown in (c), though motion is not immediately recognizable. After magnitude scaling (d) to reduce k y-dependent intensity fluctuation, and smoothing along time (e) to further reduce high-frequency changes, cardiac and respiratory motions are visible in the final form. White arrows mark five cardiac cycles and the black arrows mark two respiratory cycles. 55

81 Figure 2.8. Widths of the navigator zone (a e) and its impact on the pseudo-projection stream (f j) during a free-breathing cardiac scan. The intensity over time of the marked pixels is superimposed on each stream (white). The narrowest navigator zone width would correspond to the conventional projection-based motion tracking using only the k y=0 readout (a, f), which revealed respiratory motion only. As higher-k y PEs were included, cardiac motion started to emerge (2nd, 3rd rows). At a width of 10% k y (d, i), both cardiac and respiratory motions were fully revealed. It resulted in a motion-sampling frequency of 38 Hz and was used to process all scans in this work. Beyond 10%, no additional motion information was revealed and respiratory motion may become degraded. All data shown in this figure originated from the same duration of the same scan, as widths of navigator zone could be freely adjusted retrospectively. 56

82 Projection Pixels AU AU AU Eigenvector 2 a Eigenvector 3 ECG Triggers b c d Time (sec) Cardiac Waveform Moving Average Peak Trough Up Cross Down Cross ECG Triggers Detected Resp. Motion Resp. Gating Window Figure 2.9. Example of the PCA-based motion extraction from a free-breathing scan. In this example, the 2nd (a) and 3rd (b) most significant eigenvectors of the pseudo-projections covariance matrix predominantly carried respiratory and cardiac motion, respectively (the 1st eigenvector carried DC signal level). The cardiac eigenvector was filtered and a moving-average-crossing algorithm was applied to generate self-gating events in c. The recorded ECG-derived triggers are also shown on (b) and (c) as the timing reference. The filtered respiratory eigenvector is shown in (d), superimposed on the pseudo-projections showing nine cycles of respiratory motion (a respiratory-dominant coil is shown, although all coils were used in motion extraction). Also superimposed is the respiratory gating window around the most frequent position of the waveform, preliminarily accepting 30% of the data. Note that the more irregular portion of the respiratory motion was preserved (first 10 seconds). 57

83 Event timing lag standard deviation with respect to ECG triggers (ms) Peak Trough Up Cross Down Cross Figure Timing errors by event type of cardiac self-gating events. Each data point represents a golden-step scan, marking the standard deviation of the timing differences between the automatically detected self-gating events and their corresponding ECG triggers. The lower, middle, and upper edges of each box indicate the 25th, 50th, and 75th percentiles, respectively. In selfgated reconstructions, the type with the lowest event interval variance was used to generate cardiac triggers. Troughs were the least variable and were selected for triggering in 12 out of the 16 scans. 58

84 Figure End-systolic and end-diastolic frames of self-gated cines (GS BH, GS FB) compared to breath-hold ECG references (ECG BH). In both SAX (a) and LAX (b) cines, small features (white arrows) were well resolved in self-gated reconstructions. Golden step acquisitions reconstructed without respiratory gating (GS FB No Resp Gating) show the effects of motion. The motion profiles visualize the time course of intensity over a line segment of the image (dashed). In golden step acquisitions, however, regions of blood flow were prone to signal inhomogeneity or loss, especially in the LAX orientation. (ECG BH: standard prospective ECG-gated breath-hold acquisition; GS BH: golden-step breath-hold acquisition with cardiac self-gating; GS FB: goldenstep free-breathing acquisition with both cardiac and respiratory self-gating.) 59

85 Figure Comparison of cine frames showing eddy current and flow-induced artifact during a cardiac cycle. (a): Reference cine (ECG BH) acquired with sequential PE, ECG gating, and breath hold. (b): golden-step breath-hold acquisition (GS BH) reconstructed using ECG gating and no self-gating. (c): the same GS BH acquisition reconstructed with cardiac self-gating. (d): goldenstep free-breathing acquisition (GS FB) reconstructed with cardiac and respiratory self-gating. Compared to the reference, signal disturbance and smearing in and around the cardiac blood pool can be seen in all three golden step acquisitions, particularly in cardiac phases where blood flow is the highest (i.e. columns 2, 5, and 6). Given that similar levels of artifact can be seen in (b) (d) regardless of the motion tracking method, the artifact is most likely independent of self-gating and due to flow effects compounded by eddy currents associated with golden step PE jumps. 60

86 Figure Comparison of sharpness measurements from the golden-step self-gated cines (GS BH, GS FB) and those of the reference cines (ECG BH). An example of sharpness profile placement is shown in (a). In (b), all sharpness measurements made on end-systolic (SYS) and end-diastolic (DIA) frame from SAX and LAX slices are included, categorized only by scan types. Measurements from SAX and LAX slices are separately compared in (c) and (d), respectively, categorized by both scan type and cardiac state. As seen in (c) and (d), the SAX sharpness measurements were slightly greater than LAX, and end-systolic and end-diastolic measurements were comparable. For all box plots, the lower, middle, and upper edge of each box indicate the 25th, 50th, and 75th percentiles, respectively, and the extremes of the whiskers cover the range of data. (GS: Golden-step; BH: breath-hold; FB: free-breathing; SAX: short-axis; LAX: long-axis.) 61

87 Figure Comparison of functional measurements from golden-step self-gated cines (GS BH, first row; GS FB, second row) and those of the reference cines (ECG BH). Obtained from regions of interests (ROIs) drawn on SAX cines, LV blood pool area (a, b, e, f), LV myocardial area (c, d, g, h), and single-slice ejection fraction (e, i) of the self-gated cines showed good agreement with those of the reference cines. Linear regressions (solid black line) are superimposed over the identity line (dashed line). P-values of Bonferroni-corrected t-test are also displayed. For each functional metric, no statistically significant difference was found between self-gated cines and reference cines at a significance level of P=0.05 (Bonferroni-corrected). (GS: Golden-step; BH: breath-hold; FB: free-breathing.) 62

88 Figure Importance of the pseudo-randomness of golden step. A 144-readout golden step acquisition (a) is compared with a 144-readout interleaved acquisition with 8 readouts per segment (d). Their resultant temporal order of navigator zone coverage is color-coded (yellow: the first readout in the navigator zone; red: the last readout in the navigator zone). The well-mixed colors in (b) indicate that the golden step covers the navigator zone in a pseudo-random and uniform manner, resulting in a steady appearance of the cardiac motion on the pseudo-projection stream (c). In comparison, the well-ordered colors in (e) indicate that the interleaved PE ordering covers the navigator zone in a structured way, resulting in a time-dependent, slow-varying change in how motion is transferred onto the projections (f). This inconsistency of appearance would make the detection of motion difficult. 63

89 Figure Mutually Prime PE scheme, where N PE and the jump size have no common factor other than 1, appears to be able to cover the navigator zone at a regular interval (Column 1 and 3). However, many such pairs lead to sequential coverage or large time gaps (Columns 2 and 4). Having to find a pair that results in regular coverage adds burden to pre-scan planning. Also, even when the coverage appears to be regular, it lacks pseudo-randomness and is in fact highly structured, as indicated by the regular patterns in the color-coded timing plots (Row 2). (RO: readout) 64

90 Figure Adapting the golden step to non-fibonacci k y grid size (N PE): for any desired non- Fibonacci N PE, the next greater Fibonacci number is used to form the k y grid, over which the golden step increment is carried out as usual. During a scan, any k y indices generated that are greater than the desired N PE are simply be skipped. The pseudo-random coverage of the navigator zone is preserved, as indicated by the lack of any regular pattern in the color-coded timing plots (Row 2). (RO: readout) 65

91 Figure Relative signal magnitude as a function of k y for several subjects. For each subject, all k-space data for each k y value was averaged. The magnitude of the averaged data was normalized to that of the central readout (k y=0). Each color represents a coil, and the thick black curve represents the average of all coils. For most cases observed, the relative signal magnitude drops to 20% at ±5% k y. 66

92 Figure Diagram of phase-encode (PE) gradients for the modeling of extraneous phase accumulation of a moving spin. Three complete TRs are shown. Labels A through B indicate echo times (where spin phase directly affect the image) and refocusing points (where spin phase should be 0). T A is the time interval between the PE and the rewinding gradients within a TR, and T B the time interval between the rewinding gradient of a TR and the PE gradient of the subsequent TR. Label Significance Spin Phase: No Flow (radian) Spin Phase: With Flow V (radian) Extraneous Phase (radian) A B C D TR 1 echo TR 1 refocus TR 2 echo TR 2 refocus e jγym1 e jγym1 0 0 j γ [y M1 (y + TA V) M1] e j γ [TA V M1] = e j γ [TA V M1] e γym 2 e j γ [ TA V M1 + (y + V (TA+TB))M2] j γ V [ TA M1 + (TA+TB) M2] e 0 j γ [TA V M1 + TA V M2] e j γ TA V [M1+M2] = e j γ TA V [M1+M2] e E TR 3 echo γym 3 e j γ [ TA V (M1+M2) + (y + 2V(TA+TB))M3] j γ V [ TA (M1+M2) + 2(TA+TB) M3] e TR i echo γym i e jγ[ T AV i 1 k M k +(y+(i 1)V(T A +T B ))M i ] i 1 e jγv[ T A k M k +(i 1)(T A +T B )M i ] Table 2.1. Extraneous phase accumulation of a flowing spin at position y with velocity along the phase-encode direction V, as a function of how long it has been in the imaging slice. As the rightmost column shows, extraneous phase accumulates over time, and as a function of the velocity (m/s) and 0 th moment of gradients (T/m sec). The accumulated phase is simulated and visualized below. (Note that the 0 th moments of i th TR, M 1, M 2, M i, may all have different signs. Refer to the previous figure for Labels A, B, C, D, E, TA, and TB.) 67

93 Figure Simulation of extraneous phase on a single spin due to PE-direction flow for several PE schemes. For all schemes (Left Column), the spin is assumed to enter the imaging slice at the first TR and continue to travel at a constant speed along the PE direction. The extraneous phase per unit speed due to PE gradient moments and flow is simulated over the first 30 TRs (blue brackets labeled with sim ) and plotted (Right Column). In the sequential scheme (Row 1), the extraneous phase is minimal. In the golden step and interleaved schemes (Row 2 and 3) where there are large PE jumps, the extraneous phase is significant and causes large phase disturbance from TR to TR. 68

94 3 SORTED GOLDEN STEP CARDIORESPIRATORY SELF- GATED CINE IMAGING 3 3 Adapted from: L. Guo, D.A. Herzka. Sorted Golden-Step Phase Encoding: An Improved Golden-Step Imaging Technique for Cardiac and Respiratory Self-Gated Cine Imaging. Submitted to: Journal of Cardiovascular Magnetic Resonance. 69

95 3.1 Abstract This work develops the sorted golden step, a new self-gated cine imaging technique that builds upon the original golden step for Cartesian self-gated imaging in the previous chapter. The greatest benefits of the original golden step were shown to be the capability of providing cardiac and respiratory motion tracking at no data acquisition cost and minimal pre-scan planning. However, it was found to be prone to the dark flow artifact due to the compounding effect of eddy current and blood flow. In practice, its use may be restricted to slices of high field homogeneity and low flow, which may exclude some slices of certain subjects. To address this issue, the present technique groups the golden step readouts into temporal segments and sorts the readouts withinsegment according to their k y values before execution, so as to reduce the phase-encode differences ( jumps ) between consecutive readouts. The properties of the sorted golden step are explored in this work, and its motion-tracking ability was tested in imaging studies of healthy human subjects. Motion depiction by the sorted golden step was highly similar to that by the original golden step, and motion tracking was effective for both cardiac motion and respiratory motion, resulting in the self-gated reconstruction of highquality cardiac cines without breath holding or electrocardiogram. The eddy current- and flowinduced artifact was virtually eliminated, even for slices with field inhomogeneity-induced banding and fast blood flow. The sorted golden step was also shown to be effective for all cardiac slices of the short-axis stack besides long-axis slices. Overall the present technique preserves all the benefits of the original golden step at scan time but without the vulnerability to artifact. And with expanded cardiac slice coverage, the sorted golden step has been shown to be a significant improvement in the effectiveness and usability for the Cartesian golden step in cardiac imaging. 70

96 3.2 Introduction The previous chapter introduced a new self-gated 2D Cartesian cine imaging technique capable of tracking both cardiac motion and respiratory motion at no cost to imaging data acquisition. In that technique, a small central portion (e.g. 5% or 10%) of the Cartesian k y grid was designated as the navigator zone, and normal imaging readouts within this region were considered sufficiently close to k y=0 to be deemed pseudo-projections, from which both cardiac motion and respiratory motion were derived and used to guide self-gated cine reconstruction. Cartesian readouts were continuously acquired during a scan, and a golden step (GS) scheme was used to order their PEs this key feature ensured that at any width of the navigator zone and any scan duration, imaging readouts would pseudorandomly fall within the navigator zone at approximately uniform intervals in both time and ky. As a result, minimal motion-related pre-planning was required because the zone width could be selected retrospectively and so could the number of cardiac phases. Because all cardiac phases were equally likely to receive data in any portion of the scan, the scan duration could also be arbitrary, i.e. it would not need to be planned with consideration to the number of cardiac phases or the segmentation scheme of k-space. In the GS work, a balanced steady-state free precession (BSSFP) imaging sequence was used for high blood-myocardium contrast and high imaging efficiency. Unfortunately, the golden step s large PE jumps between consecutive readouts and the induced eddy currents [94 96] compounded with the rapid ventricular blood flow and made the technique prone to the well-known dark flow artifact [17, 19 21], which originates from BSSFP bands and flow. It was possible to avoid such artifact by carefully adjusting the scanner field to remove or shift any band away from the region of interest, but it was often expected that high-flow slices would suffer from degraded image quality. This made scan planning more onerous and restricted the use of the technique on some slice orientations, depending on the patient anatomy. 71

97 This chapter introduces the sorted golden step (sgs), a significant enhancement to the original GS technique, which is free of the dark flow artifact. Near-center readouts or pseudoprojections are still used to extract motion for self-gating, but the golden-step readouts are grouped into temporal segments and sorted according to PE before execution. This effectively reduces the PE jumps and prevents the occurrences of the dark flow artifact while preserving the ability to track both cardiac motion and respiratory motion directly from imaging readouts. The current work also expands the application of the technique by demonstrating its effectiveness in imaging all slices of the short-axis (SAX) stack in addition to the long-axis (LAX) slices. 72

98 3.3 Methods Sequence All imaging experiments were carried out using a Cartesian balanced steady state free precession (bssfp) sequence, where gradient waveforms were designed using hardware-optimized trapezoids [86] to maximize acquisition speed. As with the original GS, the grid of PEs in an sgs scan was indexed by i PE where 1 i PE N PE, and was to be continuously and repeatedly acquired during imaging. The acquisition started with the most negative PE (i PE =1). To choose the next PE, the i PE was incremented by F N, the largest Fibonacci number less than N PE, which in turn needs to be less than or equal to the next larger Fibonacci number F N+1. After the increment, if i PE > F N+1, it was wrapped around (i PE = i PE % F N+1). If N PE < i PE F N+1, this i PE was not used but instead incremented by F N again (and then wrapped) before setting the next PE. For example, for a scan with N PE of 192, i PE is incremented by 144 after each readout, subject to wrapping if above 233. If the incremented i PE has 192 < i PE 233, it is incremented again by 144 to determine the next PE. Under such arrangement, a grid of size N PE would be fully covered once with exactly N PEmany readouts. As with the work in the previous chapter, the PEs that fell within a small central portion of k y (the navigator zone ) are deemed pseudo-projections and would later be used for motion tracking. Incrementing and wrapping by Fibonacci numbers would ensure a pseudorandom PE coverage that was approximately uniform in both time and k y, inside and outside of the navigator zone. For the current work, however, in an sgs scan the stream of readouts were divided into temporal segments of equal size (e.g. 12 per segment), and sorted within each segment according to k y. Ascending sort and descending sort alternated to avoid the sudden k y change between two segments. Such PE ordering is illustrated in Figure 3.1, where it is also compared with the original GS and the interleaved PE ordering. Though similar to the sgs, the interleaved PE ordering is 73

99 subject to large temporal gaps in the navigator zone coverage. Since it is not pseudorandom, it may also introduce temporally slow-varying intensity bias to motion measurements. A more quantitative comparison of the GS, sgs, and interleaved PE schemes is made in Figure 3.2. Ideally, a PE scheme should quickly and evenly cover the k y interval of the navigator zone. Figure 3.2 Row C shows the largest remaining k y gap within the navigator zone over time. At all practical navigator zone widths, the GS and the sgs reduces the gap size at an equal pace, which is much faster than the interleaved. Another desired property of the navigator zone coverage is that the pseudo-projections should be scattered on both sides of the k-space center (k y=0) with equal likelihood over time without repeating any PE or forming a slow-varying trend. As a metric to measure this, Figure 3.2 Row D plots the cumulative k y of navigator-zone PEs since the start of the scan. For both GS and sgs, the cumulative k y remains close to k y=0, indicating the symmetric and uniform coverage of the k y interval around the k y center. In comparison, the interleaved scheme deviates far from k y=0 at higher navigator zone widths, suggesting a bias in the sampling of k y, which leads to time-varying depiction of motion. Finally, the PE scheme should sample the navigator zone at approximately equal temporal intervals, that is, without large time gaps. Figure 3.2 Row E shows the time intervals between two consecutive pseudo-projections. The GS and sgs do not have large intervals as does the interleaved, and generally have smaller fluctuation than does the interleaved scheme at all the navigator zone widths. Thus, sorting the GS PEs into segments virtually has no impact on the motion-measurement performance in terms of these metrics Imaging Experiments Five normal subjects (3 females, mean±sd age: 29±7 years) were imaged under local institutional review board approval and with written informed consent. A 1.5T clinical system (Avanto, Siemens Medical Solutions, Erlangen, Germany) was used along with its standard chest and spine coils. All scans used a 35 flip angle and the standard half-flip angle half-tr bssfp opener [87], followed 74

100 by 100 dummy TRs to transition to the steady state. All imaging slices had a thickness of 8 mm and a readout field of view (FOV) of 300 mm covered using 192 points. The phase-encode FOV was adjusted to fit the subject size and ranged from 225 to 300 mm, covered using 144 to 192 PEs to maintain a mm 2 in-plane resolution. Depending on the slice orientation and the optimized gradient design, the TR mean±sd was 2.78±0.067 ms. For each subject, a SAX stack of 9 or 10 slices was acquired to cover the extent of the left ventricle (LV) along with a 4-chamber LAX slice. For each slice, a segmented prospectively ECGgated cine was acquired under breath hold as the image-quality reference (ECG BH), using sequential k-space segmentation with a segment size of 12 readouts, resulting in a temporal resolution of approximately 33 ms per cardiac phase. Depending on the subject heart rate, 20 to 24 cardiac phases were acquired. Following the ECG BH scan, a 60-second sgs scan was acquired under free breathing (sgs FB), using a sorting segment size of 12 readouts. Finally, for illustration and comparison, the original GS scan and/or sgs FB scans with other segment sizes were acquired for subjects and slices that exhibited strong dark flow artifact. For the free-breathing scans, the ECG triggers were recorded as the timing reference but were not used in gating. All readouts were continuously acquired and saved for offline retrospective cine reconstruction Motion Extraction and Cine Reconstruction The sgs FB scans were reconstructed retrospectively using similar techniques as in the previous chapter. In summary, readouts within the central 5% of the k y-space were considered pseudoprojections and transformed into 1D image domain. The expected ky-dependent magnitude fluctuation in time was removed from the pseudo-projection stream. To reveal cardiac motion, stream was further smoothed in time using a simple Gaussian window of a temporal full width half max (FWHM) equivalent to the acquisition time of one full k-space. A group of 10 projection pixels showing the strongest cardiac frequencies were then automatically identified, and their group- 75

101 average intensity over time was used as the cardiac gating waveform to replace the ECG. To reveal respiratory motion, the temporal smoothing was instead done using a simple running averaging window of duration equivalent to acquiring the k-space twice. Principle component analysis (PCA) was then used to identify the primary component of intensity change in time, which served as the respiratory waveform. Cardiac events were derived from the cardiac gating waveform using a moving-averagecrossing (MAC) algorithm [88], and the Trough events were used to define cardiac cycles due to its lowest timing error as shown in the previous chapter. Each cycle was divided into the same number of cardiac phases as there were in the subject s ECG BH scan. An acceptance window for the respiratory waveform, centered on the most-frequent respiratory position of the scan, was automatically found to accept 30% of all readouts. These readouts were binned into the cardiac phases, and then further binned by PE. A second layer of similarity-based data sorting was used to further reduce the risk of admitting extraneous readouts: if a cardiac-pe bin contained more than one readout, only the readout whose corresponding pseudo-projection was the most similar to the mean pseudo-projection of the cardiac phase was admitted for final image reconstruction. The filled k-space for each cardiac phase was then inverse Fourier-transformed to image domain. No measure such as parallel imaging or iterative image reconstruction was used to compensate for possible missing k-space readouts, so that the motion-tracking ability of the proposed technique could be evaluated directly. For appropriate comparisons against the ECG BH images, averaging of multiple readouts within a bin was avoided though certainly feasible. For consistency, the ECG BH cines were also reconstructed offline by applying direct inverse Fourier transform to the raw k-space data of each frame, as opposed to being reconstructed directly on the scanner, where manufacturer s filters could be automatically applied. 76

102 3.3.4 Image Quality Evaluation Cardiac functional metrics as measured by the ECG BH and self-gated sgs FB cines were determined and compared: each stack of SAX cines were loaded into Seg3D (Center for Integrative Biomedical Computing, University of Utah) where, for the end-diastolic and end-systolic frames, the LV blood pool and myocardium were semi-automatically delineated using Otsu s method and intensity-based region growth in 3D. This yielded end-diastolic volume (EDV), end-systolic volume (ESV), ejection fraction (EF), and end-diastolic myocardial volume (EDMV). Image sharpness of the LV blood-myocardium border was also measured for the ECG BH and sgs FB cines, using an intensity profile-based method [61]: on each end-diastolic frame and end-systolic frame, three straight lines were drawn across the blood-myocardium border, perpendicular to the boundary, on the septal wall where it was free of papillary muscles and trabeculae carnae. On each profile, the minimal and maximal intensities were found, along with the distance (in mm) required for the intensity to transition from 20% to 80% between the minimum and the maximum. The inverse of the average of the three transition distances was considered the sharpness of the image. This process was repeated for mid-ventricular SAX slices and all LAX slices. For both functional and sharpness metrics, the paired Student s t-test was used to determine any statistical difference between ECG BH and sgs FB cines, using a two-sided statistical significance threshold of

103 3.4 Results Motion Tracking Typical sgs pseudo-projection streams can be seen in Figure 3.3, which also compares them with those generated by the original GS. Both cardiac motion and respiratory motion are visible at all sorting segment sizes. At any particular navigator zone width, different segment sizes appear to reveal motion equally well. At any segment size, a lower navigator zone width appears to better reveal motion. At 5% navigator zone width, in particular, all practical segment sizes have clearly revealed motion. The motion as depicted by sgs does not seem to be visibly different from that by the original GS. The automatic extraction of cardiac motion and respiratory motion (Figure 3.4) was successful for all scanned subjects at all imaging slices. As an enhancement to our prior GS work, the same pseudo-projections were processed differently to best reveal cardiac motion (Figure 3.4a) and respiratory motion (Figure 3.4c) separately. As a result, the two types of motion were the most dominant intensity variation on their respective pseudo-projection streams and were effectively captured by the MAC algorithm (Figure 3.4b) and PCA (Figure 3.4d) with less cross-contamination Image Quality The retrospective self-gated cine reconstruction was successful for all scanned subjects, and the reduction of the dark flow artifact was dramatic. Even for cases with severe PE jump- and flowinduced artifact (Figure 3.5), sorting readouts into segments of 4 immediately eliminated most of the artifact. At 8 or more readouts per segment, the artifact was unnoticeable. Several additional instances of such artifact reduction in slices where the artifact was prominent are shown in Figure 3.6. The same behavior held for all cardiac phases and both SAX and LAX slices (Figure 3.7), resulting in high-quality sgs FB images as compared to the ECG BH scans. The clear visualization 78

104 of small features such as the trabeculae carnae demonstrates the effectiveness of motion tracking even at time points with significant motion such as systole. Quantitatively, the cardiac functional metrics derived from the sgs FB scans showed good agreement with those from the ECG BH scans (Figure 3.8). The two kinds were found not to be statistically different at a significance level of 0.05 (Table 3.1). The blood-myocardium sharpness measures of the sgs FB images were in general slightly reduced relative to those of the ECG BH scan (Figure 3.9, Table 3.2). The reduction was small but statistically significant (P-value < 0.05). The end-systolic sharpness in general appears to be less than that of end diastole, presumably due to the high rate of myocardial motion at end systole. 79

105 3.5 Discussion and Conclusion We have introduced a significant improvement to the original golden step that is free of the dark flow artifact and capable of producing high-quality self-gated cines. As with the original golden step, both cardiac motion and respiratory motion can be captured at no additional cost at acquisition time. A key advantage of the original GS is minimal motion-related pre-scan planning: the navigator zone can be retrospectively set to arbitrary widths and it is always pseudo-randomly and evenly covered by readouts. This feature is preserved in the proposed technique, except for a single parameter: the number of readouts per sorting segment needs to be determined prior to the scan. However, in our experience, 8 readouts per segment would effectively eliminate even very severe dark flow artifact (Figure 3.6). Thus 8 can be used as a default setting for most scans. Should an imaging slice be found particularly problematic, i.e. a BSSFP band in or near the imaging slice is confirmed with interleaved-pe scans [19 21] and does not respond well to shimming or frequency shifting, then 12 or 16 readouts per segment can be used instead. One can freely choose a segment size for each scan in an imaging study, knowing all scans can be reconstructed using the same motion-extraction pipeline. Given how frequently banding and dark flow artifact appear in cardiac imaging and how they would restrict the use of the original GS, the requirement to choose the segment size prior to scanning is a small compromise Technical Considerations During post-processing, the separate generation of cardiac and respiratory pseudo-projection streams (Figure 3.4a and c) reduced cross-contamination in the automatically extracted motion waveforms. For the temporal smoothing of pseudo-projections, a simple Gaussian window and a simple running-average window were used for cardiac motion and respiratory motion, respectively. 80

106 Although one can design digital filters that adapts to the subject s heart rate and respiratory rate, in our experience the simple fixed windows were very adequate in performance. During k-space data selection for image reconstruction, only one readout was admitted by similarity-based data sorting to each PE position of each cardiac phase. This was intended to maintain a fair comparison with the ECG BH images, which only had only one readout per PE position. In practice, if the scan length provides abundant data relative to the number of cardiac phases reconstructed, more than one readout can be admitted, at least to some of the PE positions. By averaging multiple readouts per PE position, the final image SNR is boosted. Of course this may come at a cost to image sharpness. Because respiratory motion is complex, even with gating and similarity-based data sorting, some discrepancy in motion state may be present among the multiple admitted readouts per PE. However, with the flexibility of golden step, one can arbitrarily control the scan length and data availability, either at scan time or at reconstruction time (arbitrary subsections of the scan can be used for reconstruction). In other words, one can freely and smoothly trade off image SNR against sharpness. As with most published free-breathing cine techniques, the image sharpness of the gated free-breathing scans was slightly lower than the breath-hold reference due to the complex nature of the respiratory motion, which ideally would require much more complex approaches to address rather than simple gating, and may well be a separate area of research on its own [48, 62, 91 93]. However, coming at no acquisition cost, the performance of respiratory tracking in this work is solid and robust, and the high accuracy of sgs-derived functional metrics suggests that the bulk of routine cardiac MR exams can benefit from this technique Extensions and Future Work As seen in Figure 3.3, the number of readouts in a sorting segment does not visibly affect the depiction of motion, although very large readouts per segment would result in large temporal gap 81

107 in the coverage of the navigator zone and is therefore not advisable. Widening the navigator zone may alleviate this problem, but as Figure 3.3 shows, a high navigator zone width resulted in poor depiction of motion, presumably because higher PEs contain weaker signal relative to noise, and scaling up their magnitude during magnitude correction could amplify noise. Although the constant-threshold navigator zone appears to work well as proposed in this work, a dynamic navigator zone can be devised to temporarily relax or tighten the zone boundary depending on the current temporal gap in navigator zone coverage, so as to balance temporal coverage and noise amplification. It is noteworthy that the proposed technique can be adapted to perform non-rigid respiratory motion correction. With golden step, in any temporal portion of the scan, the ky-space is approximately uniformly populated. One may run a narrow sliding window of, for example, 72 readouts ( 200 ms) across the entire scan and reconstruct a low-snr image for each window position using rate-2 parallel imaging or compressed sensing techniques. Such images may not be of diagnostic quality but can be used for non-rigid image registration. Thus one can have the nonrigid deformation state at any point during the scan, and may use such information to correct imaging data acquired around that point. Comparing to respiratory gating, which discards a large amount of data outside the gating window, the motion correction would allow more data to be used in image reconstruction, therefore shortening total scan time and/or enhance image SNR. Moreover, cardiac self-gating can be simultaneously performed, using the same data stream and same process as described in the Methods section. Overall, the sgs FB image quality was found to be comparable to the ECG BH cines at all imaging slices. More importantly, the sgs is free of the frequently observed bssfp dark flow artifact, which was mild in about 50% of the SAX slices and rather prominent in about 75% of the LAX slices in prior experience with GS (see Chapter 1). We have also shown the successful sgs cardiac and respiratory motion tracking in all slices of the SAX stack. Thus, whereas the original 82

108 GS may be restricted to subjects and slices where the artifact is minimal, the sgs is not restricted to any particular types of orientation or slice and can therefore be applied to broader clinical use Conclusion A significant improvement has been made to the Cartesian golden step pseudo-projection imaging technique. The sorted golden step technique has maintained the flexibility of the original golden step and its ability to produce high-quality cardiac function studies from free-breathing ECG-free scans, without the artifact induced by the combination of eddy currents and flow observed in both SAX and LAX imaging orientations. With effective motion tracking demonstrated on all slices of the SAX stack, this technique has been shown to greatly enhance the reliability and usability of the Cartesian golden step in cardiac imaging. 83

109 Normalized ky Golden Step Central 5% Navigator Zone Widths: Central 10% Central 15% Readouts (ROs) Motion-Tracking ROs Navigator Zone Readout Number Sorted Golden Step 8 ROs/segment Sorted Golden Step 12 ROs/segment Interleaved 8 ROs/segment Interleaved 12 ROs/segment Figure 3.1. Comparison of Cartesian phase-encode (PE) schemes. In each row, a Cartesian k y grid with 144 evenly spaced PEs is covered exactly once by a particular PE scheme. In each column, the navigator zone of a specific width (red dashed) selects low-pe readouts for motion tracking (red squares). Row 1: the original integer golden-step scheme provides pseudorandom navigatorzone coverage that is approximately uniform in both time and k y. Row 2 and 3: the golden-step PEs are sorted into temporal segments of 8 and 12, respectively, significantly reducing PE jumps while preserving the pseudorandom coverage of the navigator zone in both time and k y. Row 3 and 4: If a similarly segmented PE scheme like the interleaved scheme were to be used instead of golden step, there would be large temporal gaps in the navigator zone coverage. The motion-tracking readouts would also have temporally structured and slowly varying intensity, causing timedependent bias in motion measurements. 84

110 Figure 3.2. Comparison of metrics of the golden step (GS), sorted golden step (sgs), and interleaved phase-encode (PE) schemes. Row A: the three PE schemes over time in one complete acquisition of a 144-PE k y space. Row B: PEs inside the navigator zone. Row C: the largest remaining k y gap within the navigator zone over time, note that just like GS, the sgs quickly reduces the gap size, much faster than the interleaved. Row D: cumulative k y of navigator-zone PEs, note that both GS and sgs remain close to k y=0, indicating the symmetric and uniform coverage of the k y interval of the navigator zone. In comparison, the interleaved scheme deviates far from 0 at higher navigator zone widths, suggesting a bias in the sampling of k y, which leads to time-varying depiction of motion. Row E: time intervals between two measurement of the navigator zone, note that the GS and sgs do not have large intervals as does the interleaved, and generally have smaller fluctuation than does the interleaved scheme. 85

111 Figure 3.3. Streams of pseudo-projections for motion tracking. (a) The generation of pseudoprojection streams starts with the normal Cartesian imaging readouts with k y within the navigator zone. To reveal motion, the expected k y-dependent magnitude variation is corrected, and the pseudo-projections are smoothed in time. (b) The effects of segment size and navigator zone width on pseudo-projections: sorted golden step with various segment size are compared to the original golden step at typical navigator zone widths. Both cardiac and respiratory cycles are visible at all practical segment sizes, but generally more clearly at lower navigator zone widths. Note that the streams shown here were processed to prioritize cardiac motion; respiratory motion could also be highlighted using the same data (see the following figure). ROs: readouts. 86

112 AU Pixels AU Pixels 1 a b Motion-Tracking Pixels Cardiac Waveform Moving Average Peak Trough Up Cross Down Cross ECG Triggers c Respiratory Waveform Respiratory Waveform Gating Window d Time (sec) Figure 3.4. Cardiac and respiratory motion extraction from pseudo-projections. The central 5% phase encodes (pseudo-projections) were processed for optimal cardiac motion detection (a). From a group of automatically detected cardiac pixels (red + markers), the cardiac waveform was derived and was used to generate cardiac events (b) to replace ECG triggers (dashed, shown for reference). The same pseudo-projections were processed for optimal respiratory motion detection (c), from which a respiratory waveform was extracted using principle component analysis (PCA) to perform respiratory gating (d). In the shown scan, the subject was instructed to breath-hold for several seconds before breathing freely. The flat region at the beginning of (d) shows that noncyclical motion can be captured. AU: arbitrary 87

113 Figure 3.5. Comparison of images acquired at various number of readouts per segment. A BSSFP off-resonance band near the imaging slice, which is not observed on the ECG-gated breath-hold reference cines (ECG BH, Row 1) due to its sequential PE, caused severe flow artifact (white arrows) with the original golden step (Row 2) due to the compounding effects of large PE jumps and flow. The artifact is significantly reduced when readouts are sorted into segments of ascending or descending PEs (sgs FB, Row 3 5). At more than 4 readouts per segment, the artifact becomes essentially unnoticeable. BSSFP: balanced steady state free precession. PE: phase encode. RO: readout. SAX: short axis. LAX: long axis. 88

114 Figure 3.6. Comparison of the golden step and sorted golden step acquisitions in artifact-prone slices. In some slices of some subjects, the main field inhomogeneity and blood flow are significant enough to compound with the eddy current induced by the original golden step s large phaseencode jumps, forming the dark flow artifact of bssfp (Row 1). However, the same slice can be imaged virtually free of the artifact using the sorted golden step (Row 2, using 12 readouts/segment). The sorted golden step has dramatically reduced, if not entirely eliminated, the artifact in all problematic slices encountered in this study. Four such slices from three subjects are shown here. 89

115 Figure 3.7. Visual comparison of cine image quality. Eight frames from a 24-frames free-breathing ECG-free self-gated sorted golden step cine (sgs FB) acquired with 12 readouts per segment are compared with the references cine (ECG BH) acquired with ECG gating, breath hold, and sequential PEs (also 12 readouts per segment). Several representative slices of the SAX stack at different levels (apical, mid-ventricular, basal) and a 4-chamber LAX slice are shown. Mild ghosting and blurring may be visible on some sgs images but all are free from flow- and eddy current-induced dark flow artifacts. SAX: short axis. LAX: long axis. 90

116 sgs FB (ml) sgs FB (ml) sgs FB (%) sgs FB (ml) a EDV y=0.937x R 2 = ECG BH (ml) b ESV y=0.972x R 2 = ECG BH (ml) c EF y=0.950x R 2 = ECG BH (%) d EDMV y=0.972x R 2 = ECG BH (ml) Figure 3.8. Comparison of LV functional metrics as measured from ECG BH and sgs FB images. As measured from the SAX stacks, (a) the end-diastolic volume (EDV), (b) end-systolic volume (ESV), (c) ejection fraction (EF), and (d) end-diastolic myocardial volume (EDMV) of the freebreathing self-gated sorted golden step (sgs FB) images show good agreement with those of the ECG-gated breath-hold references (ECG BH), with average absolute errors of approximately 5% or less. LV: left ventricle. EDV (ml) ESV (ml) EF (%) EDMV (ml) ECG BH 100.9± ± ± ±20.6 sgs FB 97.0± ± ± ±20.4 Difference 3.9± ± ± ±3.9 P value Table 3.1. LV functional metrics measured from ECG BH and sgs FB images. ECG BH: ECGgated breath-hold reference cines. sgs FB: free-breathing self-gated sorted golden step cines. EDV: end-diastolic volume. ESV: end-systolic volume. EF: ejection fraction. EDMV: end-diastolic myocardial volume. LV: left ventricle. 91

117 Sharpness (mm -1 ) Sharpness (mm -1 ) Sharpness (mm -1 ) a ECG-BH All Data sgs-fb b SAX DIA SYS DIA SYS ECG-BH ECG-BH sgs-fb sgs-fb c LAX DIA SYS DIA SYS ECG-BH ECG-BH sgs-fb sgs-fb Figure 3.9. Comparison of LV blood-myocardium sharpness of ECG BH and sgs FB images. For each combination of slice orientation and cardiac phase, the sharpness of the free-breathing selfgated sorted golden step (sgs-fb) images is in general similar though slightly lower than that of the ECG-gated breath-hold (ECG-BH) reference images. SAX: short axis. LAX: long axis. DIA: end-diastole. SYS: end-systole. LV: left ventricle. Sharpness SAX DIA SAX SYS LAX DIA LAX SYS (mm 1 ) ECG BH 0.496± ± ± ±0.030 sgs FB Difference P value 0.447± ± ± ± ± ± ± ± Table 3.2. LV blood-myocardium sharpness of ECG BH vs. sgs FB images. ECG BH: ECG-gated breath-hold reference cines. sgs FB: free-breathing self-gated sorted golden step cines. SAX: short axis. LAX: long axis. DIA: end-diastole. SYS: end-systole. LV: left ventricle. 92

118 4 SIMULTANEOUS T 2 PREP AND RESPIRATORY MOTION TRACKING FOR CARDIAC MRI 4 4 Adapted from: L. Guo, D.A. Herzka. Simultaneous T2 Prep and Projection-based Motion Tracking for Free-Breathing Cardiac MRI. Submitted to: Magnetic Resonance in Medicine. 93

119 4.1 Abstract T 2-weighted contrast is one of the most used contrast mechanisms in MRI and is widely used in virtually all parts of the body. In the heart, T 2 contrast is critical for the evaluation of myocardial health. As seen throughout previous chapters, respiratory motion is a major challenge to cardiac MRI due to its impact on image quality and the costliness of motion tracking. In contrast with previous chapters, this work applies to static single-frame imaging of the heart, because the generation of a specific contrast during imaging typically takes considerable time and prevents continuous multi-frame imaging. T 2-weighted imaging is no exception, where episodes of imaging data acquisition must be spaced on the order of 1 second apart to allow signal recovery. As a result, this work cannot use the projection-based motion tracking methods developed in the previous chapters. In this work, we propose a technique combining the classic T 2 preparation (T 2 Prep) module and motion-measurement readouts to achieve respiratory tracking in free-breathing scans without using traditional diaphragm navigators. In summary, multiple balanced volumetric projections were inserted into the time gap between the refocusing pulses of T 2 Prep, and the temporal stream of such projections was used for motion gating. To assess image quality and motion tracking, T 2-weighted balanced steady-state free precession scans were performed on static and moving phantoms, as well as normal human subjects and swine with acute myocardial injury. Phantom experiments showed that as many as six projections could be inserted into a T 2 Prep module with 40 ms TE while still maintaining very high image quality (<2% relative root-sum-square error at the center of the field of view). Gated reconstructions were successful for all subjects, with image sharpness and contrast-to-noise ratio comparable to standard T 2-prepared breath-hold references. This new technique has been shown to be effectiveness and holds promise for further development with greater variety of inserted motion readouts and broader applications beyond cardiac imaging. 94

120 4.2 Introduction T1 and T2 As discussed in the Introduction Chapter, an MR image is a map of the transverse magnetization in the imaged slice or volume. When the magnetization is tipped into the transverse plane from the longitudinal axis (z-axis), however, it immediately starts to evolve, or relax : it grows back along the z-axis while simultaneously decay in the transverse plane. It is important to note that the rates of the longitudinal recovery and the transverse decay are independent. In other words, the longitudinal component of the magnetization recovers while the transverse component decays, at different rate from each other. Both the recovery and the decay follow exponential trends, and their time constants are known as T 1 and T 2, respectively. An illustration of the T 1 and T 2 relaxations can be found in Figure 4.1. Mathematically, the evolution of the magnitude of the longitudinal magnetization, M z (t), can be expressed as: M z (t) = M z (0 + ) + (M 0 M z (0 + )) (1 e t T 1 ) = M 0 (1 e t T 1 ) + M z (0 + )e t T where M 0 denotes the magnitude of the longitudinal magnetization at equilibrium, and M z (0 + ) that the longitudinal magnetization immediately after the RF pulse. Note that if an =90 RF pulse is applied, M z (0 + ) would be 0; otherwise it is M 0 cos( ). Similarly, the evolution of the magnitude of the transverse magnetization, M xy (t), can be expressed as: M xy (t) = M xy (0 + )e t T where M xy (0 + ) denotes the magnitude of the transverse magnetization immediately after the RF pulse. The longitudinal recovery, or T 1 relaxation, is due to the spin s interaction with the surroundings, hence it is also known as the spin-lattice relaxation. In comparison, the transverse 95

121 decay, or T 2 relaxation, is due to a spin s interaction with the nearby spins, hence it is also known as spin-spin relaxation [103]. Aside from the quantum mechanics of relaxation, it is important to note that different biological tissues have very different T 1 and T 2 values. In fact, the same physiological tissue may have altered T 1 and T 2 values when it is diseased. Therefore, it is important to be able to visualize the T 1 or T 2 values in MR images, so that different types of tissues can be distinguished, and diseased states of a tissue can be detected T1-Weighted and T2-Weighted Imaging Indeed, what makes MRI a unique and indispensable medical imaging modality is its ability to reflect T 1 or T 2 values in the images. It is very common to have the image intensity considerably dependent on the local tissue s T 1 or T 2 values; it is known as T 1- or T 2-weighted imaging, respectively [ ]. It is also possible to extract the numerical values of T 1 or T 2 from a series of carefully designed T 1- or T 2-weighted images. This is known as T 1- or T 2-mapping, which are beyond the scope of this introduction as they are active fields of research in their own right (T 1- mapping: [ ]; T 2-mapping: [58, ]) T1-weighted imaging In short, T 1-weighted imaging distinguishes tissues of different T 1 values by letting the spins spend a specific amount time in the longitudinal axis, until the T 1 recovery of different species of tissues brings about the largest difference among their longitudinal magnetizations, so that they appear in different intensities in the image. Typically, the T 1 values of the tissues to be distinguished are known, and a specific repetition time (TR) is calculated to allow the longitudinal magnetizations of the interested tissues to recover for a specific time so that the largest difference is achieved. Imaging then takes places using a short echo time (TE), so that the longitudinal magnetizations are measured as soon as they are tipped into the transverse plane, before any T 2 decay affect their 96

122 magnitudes. Note that the tissues being imaged may start with fundamentally different M 0 magnitudes because of their different proton densities, which may impact image contrast besides T 1, hence it is termed T 1-weighted imaging rather than, for example, T 1-contrast imaging. A related technique, inversion recovery (IR) [113], inverts the longitudinal magnetizations of all tissues with a 180 pulse, and waits for certain species of longitudinal magnetizations to reach zero M z. All longitudinal magnetizations are then tipped into the transverse plane and imaged immediately. As a result, the tissue with zero M z at this moment shows no signal, and is nulled in the final images. Utilizing the behavior of T 1, the ability to null certain tissues is an important capability of MRI contrast manipulation in clinical diagnosis T2-weighted imaging Whereas T 1-weighted contrast relies on the tissues different recovery rates along the longitudinal axis, T 2-weighted contrast relies on their different decay rate in the transverse plane. After the 90 RF excitation, the transverse magnetizations are kept in the transverse plane for a specific period of time (which is TE) until the different decay rates of the spin species result in the desired magnitude difference of their magnetizations. Image acquisition then takes place. In other words, knowing the T 2 values of the spin species being imaged, one controls the TE to generate the desired contrast among them. The TR is generally chosen to be long to allow full recovery of all species longitudinal magnetizations so as to remove the influence of the different T 1 recovery rates on the magnitude of their starting magnetizations. Because transverse magnetizations experience spatially-dependent variation in main field strength, they will dephase (become incoherent) while waiting for the desired contrast. To address this issue, the spin echo is typically used: a 180 RF pulse is applied at half TE to flip all spins with respect to the x- or y-axis, so that any phase accumulated on each spin due to dephasing will cancel itself by TE. At this time, imaging data acquisition must take place immediately, because further T 2 decay and dephasing will quickly degrade signal quality. This window of imaging is almost 97

123 always too short for one to collect enough k-space data to reconstruct one diagnostic-quality image. The k-space is therefore divided into multiple segments, and only one segment of k-space data is acquired at a time. Afterward, the remaining transverse magnetization is spoiled, the longitudinal magnetization is allowed to recover, and new transverse magnetization is generated with the same T 2-weighted contrast before the next k-space segment can be acquired. As a result, the entire scan will require a significant period of time. When imaging with non-spin echo techniques such as spoiled gradient echo (SPGR) and balanced steady-state free precession (bssfp), the flip angle of the excitation RF pulse is typically not 90 and the required TE is typically too short for the desired T 2 decay. The desired T 2 difference in magnitude must be created before the excitation RF, and this is achieved using the T 2 preparation (T 2 Prep), a separate sequence module executed before the excitation RF of the first imaging TR. In the T 2 Prep (Figure 4.2), the transverse magnetizations are generated by its own 90 excitation RF pulse. Like in spin echo, the transverse magnetizations are kept in the transverse plane for a pre-defined amount of time (TE of the T 2 Prep). As they decay with T 2, a series of paired refocusing RF pulses (composite or adiabatic 180 pulses [57, 114]) is applied to undo off-resonance effects. At the T 2-Prep TE, the transverse magnetizations, now carrying desired T 2 weighting, are restored to the longitudinal direction by a final RF pulse ( 90 pulse) and are ready for image acquisition at any desired flip angle and TE. Because the spins are subject to T 1 relaxation as soon as they are restored to the longitudinal axis, the endurance of the generated T 2-weighted contrast is limited, and as a result, imaging data acquisition must start as soon as possible after the T 2 Prep. Similarly, imaging data is typically acquired in separate segments, over many cycles of signal excitation, T 2 Prep, and signal recovery. 98

124 4.2.3 T2-Weighted Cardiac Imaging T 2-weighted contrast is especially desirable in the evaluation of cardiovascular system to visualize, for example, acute myocardial injury and chronic cardiomyopathies [115, 116], because such diseased tissues have altered T 2 values from the surrounding tissues. Instead of spin echo, the bssfp is preferred for cardiac imaging for its speed and high contrast-noise ratio (CNR) in the heart, thus the T 2 Prep is typically used to impart the desired T 2-weighted contrast. As with any T 2- weighted imaging, there is a period of relatively long signal recovery time between two consecutive excitations, during which no signal can be acquired. This prevents continuous acquisition of cine images, and only single-frame static images are acquired. Similar to other T 2-weighted imaging scenarios, the k-space data required for each image is acquired over multiple segments. To avoid image blurring, each segment must be acquired at the same phase during the cardiac cycle. This point of acquisition is typically chosen to be the end-diastolic phase, where the heart s intrinsic motion is minimal. This is commonly known as diastolic imaging. A T 2 Prep, followed by the acquisition of a k-space segment, is then placed during the end diastole in every heartbeat or every other heartbeat, so that the length of one or two complete cardiac cycles allows for adequate signal recovery. As discussed in the previous chapters, imaging the heart is challenging as it is under a constant mix of intrinsic cardiac motion and respiratory motion. The standard approach for tracking cardiac cycles (and synchronizing imaging to the end diastole) is to use the QRS wave on the electrocardiogram (ECG) as the trigger representing each cardiac cycle [28, 110, 117]. For respiratory motion, breath holds (BHs) are typically used, but for scans requiring longer than 10 to 20 seconds or for patients for whom BHs are simply unfeasible, a free-breathing (FB) scan is carried out with the help of the diaphragm navigator as first discussed in the Introduction Chapter. In some implementations, a pencil-beam shaped excitation is applied periodically to measure onedimensional diaphragm motion as a surrogate for cardiac displacement [58, 118, 119]. Other 99

125 implementations of the respiratory monitoring utilize a pair of intersecting slices to detect a similar 1D motion waveform [120]. Although the previous chapters have described cardiac motion tracking without the ECG, such technique is not feasible in diastolic imaging, because in order to allow signal to recover, any type of MR signal measurement is permitted only during end diastole. As discussed in Chapter 2, ECG becomes a problem because the ECG device is subject to interaction with the rapidly switching magnetic gradients during imaging, frequently resulting in distorted ECG signals that are difficult to interpret, and occasionally causing physical heating. However, in diastolic imaging, the gradients are off for most of the time during a scan, when signal recovery is underway, and more importantly when the QRS wave takes place. Thus the distortion of the QRS wave and the heating of the hardware are unlikely to happen, and the use of the ECG does not present as a major concern for diastolic imaging. While the ECG does not interfere with MR data acquisition, the diaphragm navigator is a dedicated process that requires the generation of a 2D-localized MR signal, during which no MR data can be acquired. Each execution of the diaphragm navigator typically lasts tens of milliseconds [57, 58, 119], and takes place after T 2 Prep before imaging data acquisition (Figure 4.3a). This arrangement is intended to minimize untracked motion between the navigator and imaging, albeit at the cost of delayed imaging data acquisition. As discussed earlier, the desired T 2 contrast established during the T 2 Prep immediately starts to degrade after the T 2 Prep. Any delay in imaging data acquisition causes loss in contrast. Additionally, the diaphragm navigator not only requires additional setup time prior to scanning, adding to the overhead of the imaging study. Moreover, the 2D localization of the excitation of the diaphragm navigator signal is not perfect and often affects the imaging slice by leaving residual artifacts on the final image. Given the limited accuracy of the diaphragm navigator as discussed in the Introduction Chapter, the cost of the navigator is unnecessarily high. 100

126 4.2.4 Overview of the Present Work Given the limitations of breath holding and the diaphragm navigator, an additional MR signalbased respiratory tracking method is desired. It is noteworthy that, during the T 2 Prep, the magnetization is in the transverse plane though it has not received any spatial encoding, and therefore is unsuitable for imaging. However, motion tracking with projection-based techniques does not require encoding as does imaging. This suggests that acquisition of projections for motion detection can be performed during T 2 Prep as long as the interrogation of the magnetization does not irreversibly alter it. There have been numerous reports of successful motion tracking using limited data, using low resolution images [48, 61, 62], projections of the imaged slice [49, 73, 75, 77, 121], the average signal of the imaged slice [6, 9 11, 53, 71], or some other small subsets of imaging data itself [80, 81, 122]. If limited-data motion measurements can be made simultaneously during the T 2 Prep, the need for a separate navigator would be eliminated and the delay between imaging and T 2 Prep minimized (Figure 4.3b). This would allow more T 2-weighted contrast to be captured, or it would allow a longer segment to be acquired before the contrast degrades, hence shortening the overall scan duration by some multiples of the R-R interval. Preliminary results of inserting projections into the T 2 Prep for motion tracking have been demonstrated in an earlier work [123]. In this work, the proposed technique is examined in detail. The stability of inserting multiple projection readouts into the T 2 Prep is evaluated. The motiontracking ability of this technique is demonstrated via the T 2-weighted imaging of free-breathing human subjects, and in swine models with acute myocardial infarction and radiofrequency ablation. 101

127 4.3 Methods Sequence A 2D Cartesian bssfp sequence with a standard 40 ms T 2 Prep TE was modified for this work. As shown in Figure 4.4, the refocusing RF pulses of the standard T 2 Prep consisted of one pair of nonselective MLEV-weighted composite 180 pulses (90 x, 180 y, 90 x). For the purpose of this study, each readout inserted between the refocusing pulses acquired a single physical coordinate axis only (x, y, or z-axis), each covering 400 mm field of view (FOV) in 128 pixels (oversampled to 256 points). The projection gradients were fully balanced and were designed to maximize speed given limitations in gradient amplitude and slew rate [86]. As such, at a bandwidth of 1.95 khz/pixel, the duration of each projection was just under 2 ms. When more than one projections were inserted, they were arranged consecutively in time, with the temporal midpoint of the group aligned with that of the T 2 Prep. All studies were carried out using diastolic imaging, where a T 2 Prep (with or without inserted projections) was executed at a certain delay time (TD) after each artificial or real ECG trigger, followed by a flip angle ramp-up over 5 repetition times (TR), and the acquisition of a k- space segment of imaging data using bssfp. For each segment, the centric phase-encode (PE) ordering typically used to preserve contrast was modified to avoid eddy current effects induced by the PE jumps [94]: the centric segment was separated into a positive portion and a negative portion and executed in two consecutive heartbeats. Before the acquisition of every image, N PE N RO noise samples (the same number of samples in an image) were acquired by sampling data with open receiver channels without RF excitation. This noise data was used to ensure accurate comparison between all scans of a particular subject. All imaging experiments were carried out on a 1.5T clinical scanner (Avanto, Siemens Medical Solutions, Erlangen, Germany). 102

128 4.3.2 Phantom Studies Static phantom experiments were carried out to quantify the impact of inserting projections on image quality, and moving phantom experiments were used to visualize the effects of motion on the projections and to test motion tracking. All phantom scans used a T 2-Prep TE of 40 ms, mm 2 in-plane resolution over mm FOV ( matrix size), 10 mm slice thickness, 3.05 ms TR, 35º flip angle, and 975 Hz/px receiver bandwidth. Diastolic imaging was used to mimic imaging human subjects, with simulated RR intervals of 800 ms, a trigger delay of 500 ms, and 16 bssfp TRs per k-space segment for a total of 12 segments (12 heartbeats) per image, and an acquisition window of 36.6 ms. The narrow acquisition window was explicitly chosen to minimize errors due to motion influencing comparisons between images Static Phantom Studies Three fluid-filled bottles were used together as the static phantom to provide a large object footprint in the FOV in all imaging orientations. The phantom was scanned in transversal, coronal, and sagittal slice orientations, where each slice was shifted slightly from the isocenter (no more than 5 cm) to capture as much of the phantom as possible. For each slice, three scans were acquired with one, three, and six projections inserted along a physical coordinate axis, where six was the maximum number of projections that could fit between the two refocusing pulses given the T 2 Prep TE of 40 ms (Figure 4.4b). The three-scan group was repeated for the x, y, and z-axes, resulting in nine scans per slice. For each scan, the k-space was sampled five times and averaged to reduce random noise. Although in ideal conditions one standard T 2 Prep scan would suffice as the reference for all experimental scans, a separate standard T 2 Prep scan was acquired immediately before each of the three-scan group, so as to avoid possible error induced by B 0 field drift over time. As a result, three reference scans of identical configurations were acquired for each slice. Static phantom scans were reconstructed using inverse Fourier transform, without additional signal conditioning. The images acquired with inserted projections were compared 103

129 against their respective references in three concentric square regions (sides of 7.5, 10, and 12.5 cm) centered on isocenter (Figure 4.5a). For each region on each image, the root-sum-square (RSS) of pixel-wise difference with respect to the reference was calculated, and normalized by the region s RSS intensity on the reference image to yield the relative RSS error (RSSE). To estimate the baseline or background level of such error, relative RSSEs over the same regions were also calculated for each possible image pair of the three identical reference scans acquired for each slice. The three values were averaged and considered the background relative RSSE for the slice Moving Phantom Studies For moving phantom experiments, a single fluid-filled bottle was used. One end of the phantom was displaced vertically by a balloon, which was inflated and deflated periodically by a handoperated air pump at a frequency similar to that of respiratory motion, producing displacements of up to 5 cm. The resultant tilting motion had its main component along the y physical coordinate axis, thus in motion scans each T 2 Prep acquired 6 consecutive projections along the y-axis. The maximal number of projections were inserted to observe projection quality as a function of their placement within the T 2 Prep. Each motion scan ran continuously for 8 complete k-space repetitions over 77 sec. Following the imaging experiments, raw data from the six projections were extracted into six separate streams. Each projection was transformed to the 1D image domain for visual examination and motion tracking. To examine possible dephasing-induced signal loss over the six projections (a function of position within T 2 Prep), the total magnitude for each stream was calculated by summing the projection k-space center magnitude over the entire scan. Gated images of the motion scans were reconstructed retrospectively in a two-stage process. The first stage was imaging data gating using a 1D waveform. For each T 2 Prep, all projection readouts as measured on all receiver channels were concatenated into one extended projection (EP) of length N pt N pj N c, where N pt, N pj, and N c are the numbers of points in a 104

130 projection, projections in a T 2 Prep, and receiver channels, respectively. Principal component analysis (PCA) was used to extract the most significant component of EP variation over time [47]. The resultant 1D waveform was used in gating, whereby an acceptance window centered on the waveform s most-frequent position was automatically generated to preliminarily accept 30% of the EPs. The corresponding k-space segments were admitted to the next stage of selection. In the second stage, all window-admitted EPs were ranked based on their similarity (in the sum-squaredifference sense) to their group mean. Then, the k-space of the final image was filled only with the k-space segments whose corresponding EPs were the most similar to the mean. The final k-space of each receiver channel was inverse Fourier-transformed and combined in the complex image domain using root-sum-square Normal Human Subject Imaging Studies Five normal subjects (3 females) were imaged with local institutional review board approval and written informed consent. The standard chest and spine arrays were used, adding to a total of five receiver channels. All human scans used 256-point readouts covering 300 mm FOV, with receiver bandwidth of 975 Hz/px, slice thickness 10 mm, flip angle 90º, TR 3~3.1 ms, and TE at exactly TR/2. Depending on the subject, 192~240 readouts were acquired over 225~280 mm phase encode FOV to maintain mm 2 in-plane resolution. Similar to phantom experiments, the T 2 Prep TE was 40 ms for all scans, and ECG-gated diastolic imaging was used with trigger delays of 600~800 ms, and segments of 16~24 TRs so that each breath-hold scan could be completed in about 12 seconds. A mid-ventricular short axis (SAX) slice and a 4-chamber long axis (LAX) slice were imaged for each subject. Three scans were carried out for each slice: a reference scan (Standard T 2 Prep, BH), a breath-hold scan with one projection on each physical coordinate axis (hereafter 105

131 referred to as T 2 Prep 1x1y1z BH ), and a free-breathing scan with the same projection insertion ( T 2 Prep 1x1y1z FB ). By acquiring both BH and FB scans incorporating the combined T 2 Prep and motion-tracking projections, the effects of inserting projections and gating could be separated. As shown in c, one projection per axis was inserted so as to capture possible motion components along all axes without having to plan for the orientations of the projections. Each free-breathing scan acquired six complete repetitions of k-space in about 72 sec. The BH and FB scans were reconstructed using the same techniques described above for static and moving phantom scans, respectively Image Quality Evaluation The images of the reference and T 2 Prep 1x1y1z FB scans were evaluated for sharpness: three line segments were manually drawn across the left-ventricular (LV) blood-myocardium boundary on the septal wall, which was free of papillary muscles and trabeculae carnae. Within each line segment, the distance (in fractional pixels) needed for the image intensity to rise from 20% to 80% dynamic range was found. The inverse of the average of the three distances was considered the sharpness [11, 61]. The images of the reference, T 2 Prep 1x1y1z BH, and T 2 Prep 1x1y1z FB scans were evaluated for contrast-to-noise ratio (CNR): one region of interest (ROI) was drawn in the myocardium on the septal wall and one in the LV blood pool, and the difference between the two regions mean intensities was divided by the image-domain noise. The noise was measured by the intensity standard deviation of a noise image, obtained by reconstructing the noise samples collected at the beginning of each scan as a 2D image using the same pipeline as normal image reconstruction. The CNRs of the T 2 Prep 1x1y1z BH and T 2 Prep 1x1y1z FB scans were normalized by those of their reference scans to yield relative CNRs. 106

132 4.3.4 Swine Studies To demonstrate T 2 contrast visualization in practice, two swine were imaged. One animal underwent epicardial radiofrequency ablation on the same day of imaging. The second received a reperfused acute myocardial infarction induced by left anterior descending coronary occlusion (2 hrs) performed two days prior to imaging. In both animals, the acute injuries were expected to produce significant changes in tissue T 2 due to the accumulation of edema [112, 124]. The same scans and procedure for image reconstruction as for human subjects were performed. To delineate the true extent of the lesions, gadolinium delayed-enhancement inversion recovery scans and black-blood turbo spin echo (TSE) scans were also performed in the same scan session. Resultant images were qualitatively compared. 107

133 4.4 Results Phantom Experiments The static phantom images with one to six projections inserted can be found in Figure 4.5 and Figure 4.6. The insertion of projections caused no visible impact to image quality, except that at the highest number of projections inserted along the x and y-axes there was some signal loss in the outer FOV. Quantitatively, the relative RSSE was small in the region close to the scanner isocenter, at less than 2% for any number of projections along any axis and at a level similar to the background RSSE (Figure 4.7). The relative RSSE appeared to increase with distance from isocenter, and with number of projections inserted. The motion of the moving phantom was clearly revealed by any of the six projection streams (Figure 4.8a f). The total signal magnitudes of the six projection streams were very similar to one another, and so were the appearance of motion. As expected, the total signal magnitude appears slightly higher near the T 2 Prep midpoint, where spins are coherent due to the formation of the spin echo. The automatic motion extraction and gating were effective, and the phantom image quality was preserved (Figure 4.8g j) Human Subject Experiments Figure 4.9a c illustrate the human respiratory motion as revealed on the projections inserted along the x, y, and z axes, showing motion components in all three axes. As seen in Figure 4.9d g, the inserted projections did not visibly impact image quality. Motion extraction and gating using projections from all three axes adequately removed motion effects in the final image Figure 4.9h k. Quantitatively, the sharpness of the gated free-breathing images showed good agreement with the references (BH standard T 2 Prep), in both SAX and LAX slices for all subjects imaged Figure 4.10b c. The insertion of projections alone (T2P 1x1y1z BH) minimally impacted relative CNR 108

134 (near 100%, Figure 4.10e f). With free breathing and gating (T2P 1x1y1z FB), relative CNR was mildly degraded to about 90%, likely due to the occasional missing k-space data after gating Swine Experiments Similar to human images, swine images showed effective preservation of image quality and motion gating Figure The extent and location of visualized injury were consistent with those seen on the delayed-enhancement and black-blood TSE scans, for both the radiofrequency ablation Figure 4.11a and the myocardial infarction Figure 4.11b. 109

135 4.5 Discussion and Conclusion The respiratory motion-tracking ability of the projection readouts inserted into the T 2 Prep has been demonstrated. Both phantom motion and human breathing were clearly captured by the projections with good signal quality, leading to effective gated image reconstruction of free-breathing scans with excellent relative CNR and sharpness. The need for a separate navigator was eliminated Technical Considerations The insertion of projections minimally impacted image quality, especially near the scanner isocenter where the relative error was just a few percent, approaching the background error Figure 4.7. Signal loss was visible only at the highest number of projections inserted along specific axes (x, y-axes, Figure 4.6). The spatial pattern and the repeatability of signal loss suggest that the cause was likely gradient hardware, which might have left spatially varying residual phase in the imaging volume after gradient rewinding. Such error may compound after several consecutive projections and produce noticeable pattern in images. Indeed, gradient error near the center of k-space is a wellknown issue in radial imaging that may cause signal loss [64, 65, 125, 126]. However, even with gradient error, the signal loss was slow-varying and appeared only at outer FOV. In practice, imaging would often focus on a small FOV near isocenter, where projection-induced error was just a few percent and visually unnoticeable (Figure 4.7). In the moving phantom experiments, motion was clearly revealed across the six projections, with virtually no difference in signal appearance or magnitude (Figure 4.8). On the other hand, in human scans, where conditions are less ideal due to the heterogeneity and depth of the body, less consistency across multiple projections can be expected. However, as seen in phantoms, more than one projection per axis may not provide additional information and high number of projections may degrade the outer FOV. Thus, one projection per axis is likely optimal for respiratory gating, as motion is captured along all three axes without pre-scan planning. Note 110

136 that on 3.0 T systems, where T 2 Prep utilizes the longer adiabatic pulses [57, 112], there may be limited time for motion tracking, though the insertion of three projections would be possible with T 2 Prep TEs 40 ms. The combined preparatory sequence composed of T 2 Prep and projections for motion compensation achieves its aim, which is to remove a separate motion-tracking module such as the diaphragm navigator and the associated pre-scan planning. In this work, the reference T 2 Prep scans were carried out under breath hold rather than using the standard diaphragm navigation, because the diaphragm navigator is prone to platform- or subject-dependent performance variability. Hence, the breath-hold scans provided a higher standard for comparison. Avoiding the diaphragm navigator would also prevent any contrast degradation due to the delayed imaging data acquisition, making it a fair CNR comparison for the proposed technique. Although the proposed technique showed slightly lowered relative CNR, it was not necessarily lower than that of the diaphragmnavigated scans, which may lose CNR due to said delay. Additional moment nulling could also reduce the decrease in CNR by reducing myocardial signal loss induced by motion during T 2 Prep Extensions and Future Work While this study only used orthogonal volumetric projections, other types of motion-tracking readouts can certainly be inserted. Between the refocusing pulses, there is sufficient time for the spiral navigator [121, 127], the orbital navigator [128], and the floating navigator [78], as long as the gradients are rewound to adequate precision. When the T 2 Prep TE is sufficiently long, such as hundreds of milliseconds in abdominal imaging [111], low-resolution images may be acquired for motion tracking, using propeller blades [44] or radial projections [45]. For radial imaging in particular, each projection is also an imaging readout. This allows mixing T 2 Prep projections and imaging readouts for motion tracking, as the contrast difference between the two kinds is unlikely 111

137 to completely degrade image features. These techniques would also motivate the use of sliceselective T 2 Prep, which would provide more specific motion tracking in 2D slices [129]. In this work, the projection data was used retrospectively and multiple copies of k-space were acquired per imaging slice. However, this technique could easily be applied in a prospective manner, as is done with other respiratory navigator techniques, reducing scan duration and removing the need for acquisition of multiple copies of k-space. Although the proposed technique was only tested on cardiac T 2-weighted imaging, it can readily be applied to free-breathing coronary and abdominal imaging. The abdomen, for example, may have significant nonrigid motion that requires complex motion models [51, ]. The proposed technique would provide a flexible platform where many types of available motiontracking readouts can be used to measure motion to a degree sufficient for the application Conclusion A combined preparatory sequence including T 2 Prep and projections for motion tracking is effective in respiratory gating for free-breathing cardiac imaging. The impact on image quality, apparently dependent on gradient hardware precision, is minimal when used with practical configurations. There is ample development potential beyond cardiac imaging. 112

138 x z y M z = M 0 M z M xy M xy time a b c d e Figure 4.1. T 1 and T 2 relaxations of the magnetic spin. The spin at equilibrium (a), which is aligned with the scanner main field along the z-axis, is tipped into the transverse plane by a 90 RF pulse (b). Over time, the longitudinal magnetization M z(t) recovers while the transverse magnetization M xy(t) decays (c e). The recovery and decay are exponential with time constants of T 1 and T 2, respectively. Figure 4.2. The T 2 Prep. (a) The schematic of a T 2 Prep with two refocusing RF pulses. (b) The reaction of two spin species: as an example, the longitudinal magnetizations of two spin species are at rest along the z-axis (Time Point 1). After the initial 90 excitation pulse, the magnetizations are in the transverse plane (Time Point 2) starting to undergo T 2 decay at their respective rates. During the decay, the refocusing RF pulses undo any spin dephasing, until desired magnetization difference is attained (Time Point 3). Then the transverse magnetizations are restored back onto the z-axis (Time Point 4), ready for imaging at any flip angle. (c) The T 2 Prep with four refocusing RF pulses, with the key time points labeled. 113

139 Figure 4.3. Cardiac diastolic imaging with the T 2 Prep. Breath holding is not possible due to the total length of such scans. In conventional respiratory motion tracking (a), the pencil-beam navigator (diaphragm navigator) is placed after the T 2 Prep, which delays the subsequent acquisition of a k-space segment, potentially allowing some T 2-weighted contrast to degrade before imaging data collection. If motion tracking can be merged with the T 2 Prep, imaging data acquisition can begin immediately (b). This would allow more T 2-weighted contrast to be captured, or a longer segment to be acquired before the contrast degrades, hence shortening the overall scan duration by some multiples of the R-R interval. 114

140 Figure 4.4. By building motion tracking into the T 2 Prep, imaging data acquisition can begin immediately afterward (a). Fully rewound encoding gradients are inserted into the innermost pair of RF pulses of the T 2 Prep. Each readout acquires a volume projection onto a coordinate axis. To study projections of the moving phantom, 6 readouts are inserted onto one axis (b). For freebreathing human scans, one projection is inserted onto each axis (c) to cover all three axes and to sample as close to the center of the T 2 Prep as possible. 115

141 Figure 4.5. Example images of static phantoms acquired to test the impact of the number and orientation of projections on image quality. One, three, and six projections were inserted into the T 2 Prep along the x, y, and z physical coordinate axes in transversal, sagittal, and coronal imaging slices (all phantom images can be seen in the Results). Only transverse images with projections inserted along the x-axis are shown here (b d), compared against their reference image (a). The relative RSSE of each image with respect to its reference was calculated over the concentric square regions (dashed) around the scanner isocenter, with sides of 12.5, 10, and 7.5 cm. 116

142 z! Projections! Sagittal!Slice! y! Projections! x! Projections!!! z! Projections! Coronal!Slice! y! Projections! x! Projections!!! z! Projections! Transverse!Slice! y! Projections! x! Projections!!! Standard!T2!Prep! (No!Projections)! 1!Projection! Inserted! 3!Projections! Inserted! 6!Projections! Inserted!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Figure 4.6. Static phantom scans acquired to test the impact of number of projections on image quality. In Columns 2 through 4, one, three, and six projections were inserted into the T 2 Prep along x, y, and z physical coordinate axes, and transversal, sagittal, and coronal slices were imaged. Comparing to the reference standard T 2 Prep images (col. 1), only the highest number of x and y projections appear to cause signal degradation in the outer regions, and only along the z coordinate axis (coronal and sagittal slices of col. 4). Otherwise the insertion of projections does not visibly affect image quality. 117

143 Figure 4.7. Relative root-sum-square error (RSSE) of static phantom images with one, three, and six projections inserted into the T 2 Prep along the x, y, and z physical coordinate axes in transversal (tra), sagittal (sag), and coronal (cor) imaging slices. For each image, the relative RSSE error was calculated against the standard T 2 Prep reference over three concentric square regions centered on the scanner isocenter, with sides of 12.5, 10, and 7.5 cm. Using the same method, the baseline or background (Bgd) relative RSSE was also calculated from the three possible pairs of repeated standard T 2 Prep images for each slice (dashed). The error after projection insertion is very low near the isocenter for any number of projections along any axis, at a level similar to the background error. As expected, in any one region, more projections lead to increased error. (tra x: projections inserted along the x axis when imaging the transverse slice. Bgd tra: background relative RSSE of the transverse slice.) 118

144 Figure 4.8. Motion-tracking projections and final images obtained from a moving phantom. Six projections along the y coordinate axis were inserted into a 40-ms T 2 Prep, filling the entire time gap between the two refocusing pulses. The resultant projections over 90 simulated heartbeats or 72 sec are shown (a f). The total signal magnitude (readout DC-center magnitude summed over time) are comparable across all six projections, with slightly higher values near the center of T 2 Prep due to the expected spin echo refocusing. Motion is clearly revealed on all six projections, and motion can be readily extracted (dashed lines). As compared to the standard T 2 Prep reference (g), the insertion of projections did not visibly disturb the quality of the stationary image (h). The gated image (i) shows the effective removal of motion (j). (6y: six projections were inserted into the T 2 Prep along the y coordinate axis.) 119

145 Figure 4.9. Projection streams and images of a human subject. Three projections, one along each coordinate axis, were inserted into a 40 ms T 2 Prep. The projections over 90 heartbeats are shown in a c. Respiration is revealed along all axes, and the automatically extracted motion waveform (dashed) is superimposed on each. As compared to the standard T 2 Prep reference (d, e), the inserted projections did not visibly disturb image quality, for both breath hold (f, g) and free breathing (h, i). The gated reconstructions (h, i) show the effective removal of respiratory motion (j, k). (1x1y1z: one projections inserted along each axis in the T 2 Prep; BH: breath hold; FB: free breathing.) 120

146 Figure Comparison of image quality metrics. Image sharpness was measured from intensity profiles drawn on the left-ventricular blood-myocardium border (a). Comparing to breath-hold standard T 2 Prep scans, the gated free-breathing T 2 Prep scans with projections produced comparable image sharpness in both short-axis (SAX) scans (b) and long-axis (LAX) scans (c). Blood-myocardial contrast-to-noise ratio (CNR) was measured from blood and myocardial regions of interest (ROIs) (d), and normalized by the CNR of the reference scan (Standard T 2 Prep, BH) at the same ROIs. The insertion of motion-tracking projections alone (T 2 Prep 1x1y1z BH) minimally impacted relative CNR, with mean ± standard deviation of 99.5±5.42% for SAX (e) and 96.9±2.73% for LAX (f). Free-breathing scans gated with the projections (T 2 Prep 1x1y1z FB) saw mildly reduced relative CNR: 87.0±10.1% for SAX and 89.8±5.33% for LAX due to the occasional missing k-space data after motion gating. (1x1y1z: one projections inserted in T 2 Prep along each axis; BH: breath hold; FB: free breathing.) 121

147 Figure T 2-weighted contrast of cardiac lesions on two swine models: lesion induced by radiofrequency ablation applied epicardially on the same day of imaging (a), and reperfused acute myocardial infarction induced by coronary occlusion performed two days prior to imaging (b). Comparing to the standard T 2 Prep (col. 1), the inserted projections (col. 2) did not visibly impact image quality. Respiratory motion tracking was effective, and the gated reconstruction (col. 3) maintained both sharpness and contrast. As references, gadolinium delayed-enhancement inversion recovery scans (col. 4) and black-blood turbo spin echo (TSE) scans (col. 5) were performed to delineate the extent of the lesions. (1x1y1z: one projections inserted in T 2 Prep along each axis; BH: breath hold; FB: free breathing; TSE: turbo spin echo.) 122