Ultrafast Imaging: Principles, Pitfalls, Solutions, and Applications

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1 JOURNAL OF MAGNETIC RESONANCE IMAGING 32: (2010) Review Ultrafast Imaging: Principles, Pitfalls, Solutions, and Applications Jeffrey Tsao, PhD* Ultrafast MRI refers to efficient scan techniques that use a high percentage of the scan time for data acquisition. Often, they are used to achieve short scan duration ranging from sub-second to several seconds. Alternatively, they may form basic components of longer scans that may be more robust or have higher image quality. Several important applications use ultrafast imaging, including real-time dynamic imaging, myocardial perfusion imaging, high-resolution coronary imaging, functional neuroimaging, diffusion imaging, and whole-body scanning. Over the years, echo-planar imaging (EPI) and spiral imaging have been the main ultrafast techniques, and they will be the focus of the review. In practice, there are important challenges with these techniques, as it is easy to push imaging speed too far, resulting in images of a nondiagnostic quality. Thus, it is important to understand and balance the trade-off between speed and image quality. The purpose of this review is to describe how ultrafast imaging works, the potential pitfalls, current solutions to overcome the challenges, and the key applications. Key Words: ultrafast imaging; magnetic resonance imaging (MRI); echo-planar imaging (EPI); spiral J. Magn. Reson. Imaging 2010;32: VC 2010 Wiley-Liss, Inc. THE DURATION OF a scan is generally long in MRI compared with other modalities such as ultrasound and computer tomography (CT). Thus, achieving a high imaging speed while retaining a good image quality has long been recognized as important in further expanding the clinical use of MRI (1). Ultrafast imaging refers to efficient scan techniques that use a high percentage of the scan time for data acquisition. Often, they are used to achieve very short scan duration from sub-second to several seconds (1,2). Alternatively, they are used as components of a Novartis Institutes for BioMedical Research, Cambridge, Massachusetts, USA. *Address reprint requests to: J.T.,, Novartis Institutes for BioMedical Research, 250 Massachusetts Avenue, Cambridge, MA jeffrey.tsao@novartis.com Received September 15, 2009; Accepted April 23, DOI /jmri Published online in Wiley InterScience ( longer scan that is more robust or have a higher image quality. The underlying principles to achieve high imaging speed have been known for some time (3 7). Yet, it awaited a series of technical evolutions and revolutions, including gradient improvements, sequence design (8 12), reconstruction algorithm (13 18), and parallel imaging (19 21), before many of the challenges were mitigated or overcome, and the image quality reached a sufficient level for routine clinical use. Nowadays, techniques from ultrafast imaging are used on a relatively common basis. The benefits of achieving higher speeds are clear. From a practical standpoint, reducing scan time helps to improve patient comfort and compliance, thereby minimizing motion during a scan. This is particularly important for time-sensitive applications (e.g., catching realtime dynamics, scanning a patient with acute ischemic stroke [22], etc.), patients with difficulty staying still (e.g., pediatric population [4], cardiac stress testing [23]), or motion-sensitive applications such as diffusion imaging (24 29). Additionally, by reducing the duration of each scan, it may be possible to fit more scans within a session to obtain a more comprehensive examination. At higher imaging speeds, it becomes feasible to examine a wide range of relevant physiological processes or to freeze their motion that may otherwise lead to artifacts. Such physiological processes include respiration (30), cardiac rhythm (31), peristalsis (30), hemodynamics from neuronal activation (32 34), among others. For example, ultrafast imaging is often used in cardiovascular imaging (23,31,35 40), either to shorten scan duration (Figs. 1, 2), or for real-time observations (Figs. 3, 4). Ultrafast imaging poses several practical challenges. Historically, imaging speed was increased primarily through improvements in gradient performance, in terms of strength, slew rate, duty cycle, and eddy currents. These improvements have enabled reduction in scan duration by 100,000-fold, from tens of minutes to sub-second. However, gradient switching rate has reached regulated safety limits, which were established to reduce the risk for peripheral nerve stimulation (41,42). Even still, gradient improvements were insufficient by themselves to achieve satisfactory image quality in ultrafast imaging. Typically, ultrafast VC 2010 Wiley-Liss, Inc. 252

2 Ultrafast Imaging 253 images exhibit a lower spatial resolution, more geometric distortion, more blurring, less image contrast, or a combination of these degradations. In fact, it is quite easy to push the imaging speed too far, resulting in poor images with a nondiagnostic quality. Therefore, the ability to increase imaging speed further relies on a proper understanding and balance of the factors impacted by imaging speed, including image contrast, signal-to-noise ratio (SNR), artifacts, acoustic noise level, radiofrequency power deposition, and the risk for peripheral nerve stimulation. The purpose of this review is to explain how ultrafast imaging works. It grew out of the Ultrafast Imaging course from 2008 to 2010, as part of the MR Physics and Techniques for Clinicians session at the International Society for Magnetic Resonance in Medicine (ISMRM) annual conference. The review provides a more in-depth resource of the topics covered in the lecture. In the following sections, the mechanics of ultrafast imaging are described first, with a focus on the two most common techniques to acquire data: echo-planar imaging (EPI) and spiral. The key idea behind ultrafast imaging is to make the MR scanner as time efficient as possible. However, the increased efficiency comes at the cost of image quality, which will be described in the Pitfalls section. By understanding the underlying causes, it is feasible to mitigate or overcome some of the challenges. Several key applications that have been enabled or facilitated by ultrafast imaging are described. MECHANICS OF ULTRAFAST IMAGING To get a proper understanding of ultrafast imaging, it is helpful to review the process of image formation in MRI, which involves three key components (Fig. 5 top): pulse sequence, k-space, and reconstruction. During acquisition, the scanner performs a series of tasks according to a timing diagram called the pulse sequence, which dictates scanner activities such as playing out excitation pulses, turning on and off magnetic field gradients, and turning on the receivers to acquire the signals. The acquired data are arranged into a data matrix called k-space. This process is repeated until the data matrix is filled up. Then, the data are converted into an image by a mathematical process known as reconstruction. Pulse Sequence Figure 1. High-resolution free-breathing three-dimensional (3D) black-blood imaging of the right coronary artery (RCA) vessel wall, showing the anterior and the posterior walls (arrows). The broken arrows point to the contrast between the tissue in the path of the cylindrical pulse and the surrounding tissue by use of the local inversion prepulse. Imaging was performed in every other R R interval using a spiral sequence with the following parameters: TR ¼ 29 ms, TE ¼ 2.3 ms, acquisition window ¼ 59 ms, 20 slices, field of view (FOV) ¼ 400 mm, acquisition matrix ¼ , spatial resolution of mm 3, and average scan time of 12 min. Reproduced from Desai et al (103) by permission of the European Society of Cardiology. Courtesy of Matthias Stuber. The pulse sequence controls the timing of the scanner (bottom of Fig. 5). Using a gradient-echo sequence as an example, one can divide it into separate modules (see light gray boxes in bottom of Fig. 5): a signal generation module (i.e., to excite the spins) and a readout module (i.e., to acquire the data). Each module can be swapped with other choices to modify sequence characteristics. Different pulse sequences, such as a gradient-echo, a spin-echo, or balanced steady-statefree-precession (bssfp) sequence, can be viewed as different combinations of these modules. The readout module can be swapped for more time-efficient modules such as EPI or spiral, which will be the subject of discussion later on. The overall timing of the sequence determines the overall image contrast. Beyond that, one has the flexibility to modify the scanner activities in the sequence. In Figure 5, T acq indicates the acquisition window, which is the duration when the receiver acquires signals. In this example, T acq only takes up a small fraction of repetition time (TR), and there is considerable time other than the signal generation and readout modules when the scanner does not perform any tasks at all. The goal of ultrafast imaging is to minimize such idle time to improve efficiency. Figure 6 shows a comparison of a spin-echo sequence, a gradient-echo sequence, and their faster counterparts (fast spin echo and echo planar imaging, respectively). In the fast sequences (Fig. 6b,d), more than one signal is acquired per TR, so more time is used for data acquisition in each repetition. For the fast spin-echo example (Fig. 6b), additional 180-degree pulses are used to generate additional spin echoes; while for the echo planar imaging example (Fig. 6d), gradient reversals (i.e., switch gradients to negative, and then positive along the readout direction) are used to generate additional gradient echoes. In either case, the subsequent signals are smaller in amplitude, due to T 2 decay in the spin-echo case, or T 2 * decay in the gradient echo case. Typically, T2 is on the order of 40 to 100 ms for tissues, while T 2 * decay is much faster on the order of 10 ms or less. The series of echoes is called an echo train. For example, an echo train length

3 254 Tsao Figure 2. Rapid quantitation of high-speed flow jets. Short-TR spiral phase contrast in two patients with aortic stenosis: cine color flow loops and time velocity waveforms acquired in single breathholds. In these two patients, 45 cardiac phases were acquired in each 10-s breathhold, with a scan time of 22 ms per image. Selected frames from cross-sectional views of the aortic root are shown, using through-plane flow encoding. Adjacent to each are time-resolved velocity histograms, which were generated by plotting measured velocities within a region of interest (ROI) around the aorta in each slice. Peak velocities were within 20% of echocardiography measurements. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc., from Nayak et al (93). Courtesy of Krishna Nayak. of 8 indicates that 8 echoes are acquired per TR. As a result, only 1/8 the repetitions are needed, thereby reducing the total scan time to 1/8. By lengthening the echo train, the acquisition becomes more efficient beyond just eliminating the idle time. Timing overhead, such as the signal generation module, is also reduced overall. However, a longer echo train also increases the minimum TR, which has implications for sequences such as bssfp (43 45), which become more sensitive to off-resonant banding artifacts. Therefore, bssfp sequences are typically made fast by eliminating idle time only, and not by having a long readout. k-space and k-space Trajectory The data acquired in the pulse sequence are mapped onto the data matrix known as k-space (46,47) (Fig. 7) Figure 3. Real-time cardiac images from a spiral sequence at 3T, showing the right coronary artery (RCA) (see arrows). Off-resonance effects were corrected with a linear shim-perslice approach during reconstruction. The image on the right shows a susceptibility artifact (see asterisk), which obscures the distal portion of the RCA. Scan time was 120 ms per image. Courtesy of Krishna Nayak.

4 Figure 4. (Top) Long-axis image of the heart at end-systole from a cine strain-encoded (SENC) sequence acquired in a single heartbeat covering the whole cardiac cycle. The temporal resolution is 32 ms. The sequence is a special SENC with selective encoding (tagging) and spiral acquisition. The red color in the image indicates circumferential shortening in the lateral wall. The septum is akinetic due to infarction. (Bottom) The three curves in the plot are the measured circumferential strain at three locations: right ventricular (RV) free wall (red), septum (green), and left ventricular (LV) lateral wall (blue). The negative values of the curves indicate the normal shortening of the myocardium during normal contraction. Notice that while the LV free wall curve (blue) bottoms at end-systole, that of the RV free wall curve (red) bottoms much earlier, indicating interventricular dyssynchrony. The septum curve is shallow and does not dip much during the cardiac cycle, indicating akinesia. Courtesy of Nael Osman. Figure 5. (Top) Process of image formation in MRI. A pulse sequence is chosen that dictates the scanner activities and timing. The acquired data are compiled into a data matrix called k-space. When the data matrix is filled, it is converted into an image by a process called reconstruction. (Inset below) The pulse sequence diagram shows a time line of scanner activities. The scanner activities are grouped by categories. In this example, there are four horizontal lines, representing from top to bottom (i) radiofrequency (RF) activities which include excitation and signal reception, (ii) activities of the slice encoding gradient (G slice ), (iii) activities of the phase encoding gradient (G phase ), and (iv) activities of the readout gradient (G readout ). Conceptually, the pulse sequence can be viewed as consisting of modular blocks (light gray boxes). In this case, there are two modules, representing the activities for signal generation, and those for signal readout. It is implicitly assumed that the scanner repeats this time line, and the duration of each repetition is designed as the repetition time (TR). T acq indicates the duration of the signal acquisition window.

5 256 Tsao Figure 6. Comparison of a spin-echo (a), a fast spin-echo (b), a gradient-echo (c), and an echo-planar-imaging sequence (d). The time line for the slice-encoding gradient G slice is omitted to simplify the diagram. The fast versions of the sequences (b,d) differ by having additional scanner activities (shown in gray), which lead to the generation of additional echoes. The extra echoes are lower in amplitude due to T 2 decay for spin echoes (b), and T 2 * decay for gradient echoes (d). The length of the echo train is inherently limited by the signal decay. (See Appendix for further explanation of k-space). In the most common case, called Cartesian sampling, the data are mapped line by line from top to bottom of k-space, similar to the raster display of a television (48). If the user defines the image matrix to have 100 lines, the sequence will repeat 100 times, each time acquiring a different line of k-space. The choice of which line to acquire is controlled by modulating the strength of the phase encoding gradient during each repetition. If multiple echoes are acquired, the data are typically mapped onto multiple equally spaced lines to fill up more of k-space each time. The concept of k-space is important, although it may appear somewhat abstract at first. The metaphor to a physical space provides an intuitive interpretation of the process of data acquisition (46,47). Transferring the data acquired from the pulse sequence to fill up a line in k-space is akin to treating k-space as a canvas, and drawing a line through it. The goal is to draw enough lines to fill up k-space at a sufficient density as determined by the reciprocal of the field of view. With this analogy in mind, one has the freedom to fill in k-space with lines of arbitrary shapes and lengths, beyond horizontal lines only. The shapes of the lines and the speed at which they are drawn are controlled by the gradient waveforms. The collection of these readout lines is called the k-space trajectory (47). To increase imaging speed further, the central idea is to acquire more than one horizontal line of data each time, according to the chosen trajectory. The two most popular trajectories for ultrafast imaging are EPI, which acquires an alternating line of data through the data matrix (6), and spiral imaging (8,9), which acquires a curved line of data (Fig. 8). These trajectories have become popular due to certain intrinsic advantages from their geometry, such as their robustness against some artifacts (49 52) and the efficient use of gradient performance in spiral. In general, the trajectories can be of arbitrary shapes as discussed, including radial (53), square spiral (54), Rosette (55), Lissajous (56), among others. Figure 8 shows the EPI and spiral trajectories, which cover more of k-space per readout. Because each readout is longer, the entire data matrix can be covered with fewer repetitions of the longer readouts (Fig. 8, middle column). At the extreme case, the readout trajectories can cover the entire data matrix in a single shot (Fig. 8, right column). The single-shot approach is the fastest, with a sub-second acquisition time. Figure 7. The pulse sequence short-hand (left) means that the sequence of activities is repeated several times (middle). Each time the sequence is repeated, a separate signal is acquired. The signal corresponds to one line through the data matrix called k-space (right). By repeating the process and gathering the signal that correspond to different lines of k-space, one can gradually build up the entire data matrix.

6 Ultrafast Imaging 257 acquired on a rectangular grid (so-called Cartesian sampling), the inverse Fourier transform can be calculated extremely efficiently by a method called the Fast Fourier transform (FFT) (57). Otherwise, the data are typically interpolated onto a rectangular grid first (13,14,17), to take advantage of the speed of the FFT subsequently. Additional information can be incorporated in the reconstruction process to enhance the results. For example, information about coil sensitivity can be incorporated to enable parallel imaging (19 21). Effects of experimental nonidealities, such as magnetic field variation, can be accounted for during reconstruction to improve image quality, as discussed later. PITFALLS OF ULTRAFAST IMAGING Figure 8. Examples of Cartesian and non-cartesian k-space trajectories. White thick arrow represents one readout line, whereas the thin dotted lines represent other readout lines. Cartesian trajectories are those that only read data along a rectilinear grid in k-space. In a standard Cartesian trajectory (left), data are read in a raster manner, one line at a time. Fast imaging methods amount to covering more of k-space per readout. This can be achieved by winding through multiple horizontal lines during the readout (top center), or by winding through a curved line (bottom center). At the extreme, the trajectory can wind through the entire matrix in a single shot. The fast Cartesian trajectories are also referred to as echo-planar imaging (EPI). By covering more of k-space, the duration of the readout window is extended, which also increases the susceptibility to artifacts. Reconstruction The data matrix in k-space is converted to an image by a mathematical operation called inverse Fourier transform. The reason for an inverse transform (as opposed to a forward transform) is due to a sign convention (i.e., spin precession occurs clockwise, while rotation described by the formula e iangle occurs counterclockwise for increasing angle). If the data are There is an inherent trade-off between imaging speed and quality. Specifically, there are three types of degradation in ultrafast imaging: (i) increased noise, (ii) signal evolution during readout, and (iii) experimental imperfection. (Fig. 9). Pitfall 1: SNR Faster imaging speed leads to increased image noise, because there is less total time for signal reception. This is equivalent to having fewer signal averages. Specifically, the SNR is proportional to square root of the total duration used for data acquisition (58). Pitfall 2: Signal Evolution The readout is often extended to acquire more data in each repetition to push imaging speed further. By prolonging the readout, there is also more time for artifacts to arise. For example, the readout window may be one or 2 ms for a gradient echo sequence, whereas it may be prolonged to above ten milliseconds for a single-shot sequence. As shown below, this increase in several milliseconds has a dramatic influence on image quality. Figure 9. Fast imaging speed impacts image quality in three ways. Asterisks indicate solutions or workarounds that may also change image contrast. Note that increasing the field strength improves the SNR, while worsening the extent of signal evolution, so a trade-off is needed between the two opposing effects.

7 258 Tsao Figure 10. Gradient-echo images of a phantom containing water, oil, and air. The bottom row shows images at increasing echo times. For specific regions of interest (ROI) denoted as 1 to 3 in the upper left panel, their intensities at increasing echo times are shown in the upper right graph. Several factors affect the shape of these curves. T 2 * decay leads to an exponential attenuation, while B 0 inhomogeneity together with the slice profile modulates the envelope of the signal decay. Interference among signals with different chemical shifts lead to an oscillatory time course (see ROI 1 at water oil interface). Figure 10 shows a series of gradient echo images of a phantom at increasing echo times, TE, and a fixed repetition time, TR. The phantom contains a mixture of water, oil, and air, which is sufficient to reproduce many of the artifacts observed in vivo. These artifacts worsen with increasing echo times. They include susceptibility artifacts that lead to signal voids close to water air interfaces, off-resonant chemical-shift effects that lead to constructive and destructive interference between signals at different frequencies (e.g., water and fat, region of interest [ROI] 1), and T 2 * decay that leads to signal attenuation (ROI 2). Not captured in this example are additional causes of artifacts such as blood flow (49,59), patient motion, among others. By increasing the readout window, part of the data matrix will be filled with data from an earlier echo time, while others will come from a later echo time. This can be viewed as mixing parts from different images in Figure 10 to form a single image. Because the images have considerably different appearances at increasing echo times, there are inherent mismatches in the combined data. This mismatch from signal evolution is a key cause of the compromised image quality in ultrafast imaging. In general, the larger the change is during the readout, the more pronounced are the artifacts. Pitfall 3: Experimental Imperfection The third pitfall of ultrafast imaging comes from experimental imperfection, such as inaccuracy in instrumentation. As imaging speed is pushed to the limit, slight errors in timing (on the order of microseconds) or in gradient switching (e.g., from eddy currents) and slight differences in response among the X, Y, and Z gradients (60) result in position errors between the intended and actual k-space trajectories. This results in the data being misplaced from their proper locations in k-space. The impact on the image depends on the pattern and extent of those displacements. In addition to instrumentation errors, concomitant fields constitute another source of experimental imperfection. Concomitant fields are deviations between the desired and the actual magnetic field gradients (61 65), resulted from a physics principle (Maxwell equation) rather than inaccuracy in instrumentation. For example, the Z gradient does not only cause the magnetic field strength to vary linearly along the Z direction, but there are also nonlinear variations along the X and Y directions, often referred to as higher-order gradient terms. Concomitant fields are not related to imaging speed per se. However, the deviation is proportional to the square of the gradient strength, and inversely proportional to the field strength, and it results in an accumulation of phase error. Therefore, the stronger gradients and increased readout window used in ultrafast imaging increase the susceptibility to concomitant fields. Artifact Patterns Depend on k-space Trajectory Because EPI and spiral cover k-space along different trajectories, the errors from signal evolution or experimental imperfection are mapped onto k-space in different manners, thus leading to different appearances of the artifacts. On the other hand, image noise affects all of the acquired data equally, so the impact of noise is mostly independent of the k-space trajectory. Artifacts of EPI EPI acquires data along a trajectory that alternates in direction between successive lines that sweep through k-space. In the example of Figure 8, the EPI trajectory sweeps the first line from left to right, and then turns back for the second line from right to left. This process repeats itself and sweeps through k-space from top to bottom. Artifacts from signal evolution are more prominent along the direction that takes longer time,

8 Ultrafast Imaging 259 Figure 11. Gallery of common artifacts, acquired with an air/oil/water phantom at 7T to accentuate signal evolution. Full data were acquired with a 2D CSI sequence, and resampled to simulate different acquisition techniques. (Top row, a,b) gradient echo sequence with one k-space line per repetition. As the acquisition window T acq is lengthened (equivalent to reducing bandwidth) chemical shift leads to increased displacement (arrow 1). (Middle row, c e) EPI sequence. Chemical shift leads to slight displacement along the horizontal direction, but more dramatically in the slower dimension (vertical in this case, see arrow 2). B 0 inhomogeneity (i.e., shimming problems) leads to geometric distortions. Because this is a relatively well-shimmed phantom, the slight distortion can only be seen at a long T acq (arrow 3, not obvious). Strong local changes in magnetic field strengths, called susceptibility artifacts lead to local distortions, or signal voids in the extreme case (arrow 4). Misalignment in k-space by only 0.5 points leads to a Nyquist ghost, which is accentuated for illustration with the grayscale window level (arrow 5). (Bottom row, f h) Spiral sequence. Chemical shift leads to blurring of the off-resonant signals (oil in this case, arrow 5), which worsens with a longer T acq (arrow 6). This blurring can appear as a magnification ghost (arrow 6) or out of focus (arrow 7). Susceptibility artifacts lead to blurring, or signal voids in the extreme case (arrow 8). Setting the Larmor frequency deliberately at the oil frequency instead, the situation between water and oil is reversed. The brighter oil component comes focused, while the darker water component exhibits blurring (arrow 9). which, in this example, is the vertical direction. Any variation in the magnetic field strength (or precession frequency), from inadequate shimming (so-called B 0 inhomogeneity) or chemical shift, causes spatial shifts of the image signals (Fig. 11c, arrow 2). If the spatial shift varies locally, the results is manifested as geometric distortions (15) (Fig. 11d, arrow 3). In severe cases, they can lead to signal drop-outs. Such artifacts are particularly prominent close to tissue air interfaces, due to strong local variations in magnetic field strength, called susceptibility artifacts (Fig. 11d, arrow 4). For example, the orbitofrontal and parietal regions are typically problematic in functional brain imaging (32,33). The most common EPI artifacts from experimental imperfection are due to mistiming or inaccuracy in gradient amplitude, such as from residual eddy currents. Mistiming or eddy currents lead to temporal shifts in the readout, which translates into lateral shifts in k-space due to the shape of the trajectory. Consequently, the data acquired along one readout direction (e.g., from left to right) may not align exactly with those in the opposite direction (e.g., from right to left). The resultant image artifact resembles a foldover artifact, called Nyquist ghosting (66,67) (Fig. 11e, arrow 5). Concomitant fields cause deviations that are manifested as distortion, blurring, and Nyquist ghosting (65).

9 260 Tsao Artifacts of Spiral In spiral imaging, the trajectory starts from the center of k-space and moves outward. Hence, the center is acquired at a different time than the periphery. Frequency differences, such as from inadequate shimming (B 0 inhomogeneity), incorrect setting of the Larmor frequency (Fig. 11h, arrow 9), or chemical shift (Fig. 11f,g, arrows 6, 7), lead to signal evolution during the readout, which results in image blurring, or in the more severe cases, signal void (Figs. 3, 11g, arrow 8). The blurring can appear as if it is out of focus, or it can appear as a form of ghosting, referred to as a magnification ghost hereafter, with one slightly smaller version of the object superposed on a slightly larger version (Fig. 11f, arrow 6). In particular, portions of the image that are on resonance remain focused, while off-resonant portions become blurry. The degree of blurring depends on the frequency difference. Signals from blurry regions can bleed into neighboring areas (Fig. 11f,g, arrows 6, 7). In typical images that contain both tissues and fat, the inherent chemical shift between the two species (3.3 ppm) is sufficient to result in local blurring, even if shimming is perfect. Spiral is more demanding in terms of sensitivity to experimental imperfection (52,68,69). Mistiming or inaccuracy in gradient amplitude causes the acquired data to be shifted along the spiral arcs of the trajectory, which can result in blurring, a slight rotation of the image, and/or intensity variation, depending on the extent of the shift (68 70). Concomitant fields lead to an accumulation of phase errors, which results in blurring (64,68). These increased technical demands and hence the higher susceptibility to practical nonidealities have slowed the clinical adoption of spiral techniques compared with echo planar imaging (52). Overcoming the Pitfalls of Ultrafast Imaging Over the years, several solutions were developed to either mitigate or overcome the pitfalls of ultrafast imaging. Some of the solutions involve prospective adjustments, such as a calibration or changes in the pulse sequence; while others involve retrospective corrections, which operate on the acquired data and do not affect the scanning process. Tackling SNR The SNR is fundamentally related to the total duration of data acquisition. With all else being equal, shorter scans will lead to noisier images. SNR is a key limiting factor for ultrafast imaging. In practice, there are workarounds to improve SNR, such as by using optimized coils, administering contrast agent to shorten T 1 relaxation time, shortening the echo time to reduce T 2 or T 2 * decay, among others (Fig. 9). Because some of these workarounds change the T 1 and T 2 /T 2 * weighting, they also affect image contrast. Advanced acquisition (e.g., variable averaging) and reconstruction (e.g., regularization) techniques can also be used to modify SNR in a trade-off with other image attributes such as resolution and artifact level, but this topic is beyond the scope of this review. Tackling Signal Evolution by Minimizing Heterogeneity Image quality is improved by reducing the extent of signal evolution that occurs during readout. This can be achieved by tackling the underlying causes of the signal evolution, or by shortening the readout. For example, B 0 inhomogeneity can be reduced (but often not eliminated) by improved shimming (71). Frequency-selective presaturation or excitation (72) can be used to minimize variations from chemical shift, such as between water and fat. To overcome residual variations, one may acquire an additional map of the B 0 field. This field map can be incorporated in the reconstruction to correct the artifacts. For EPI, this correction amounts to unwarping the image based on the known distortion resulting from the magnetic field variation (15). For spiral, this amounts to reconstructing images at a variety of off-resonance frequencies and creating a final image that is a pixel-by-pixel composite of these images based on the off-resonance frequency at each pixel location. This process is called conjugate phase or multi-frequency reconstruction (73 75). In certain situations such as water fat imaging, the field map may already be obtained automatically as part of the procedure to separate the signal contributions from water and fat (76). Tackling signal evolution by shortening the readout Another approach to limit signal evolution is to shorten the readout itself. This can be achieved by choosing as small a data matrix in k-space as possible, but this also limits the spatial resolution. One may use stronger gradients (also known as increasing the bandwidth), but this compromises SNR, due to the shorter total acquisition as mentioned above. A third technique is to divide the trajectory into multiple shots to shorten the duration of each shot. This leads to a dramatically improved image quality (10,12). However, there is an underlying assumption with multi-shot imaging, which is that the image remains the same from shot to shot. Violation of this assumption leads to motion artifacts. Techniques such as electrocardiogram (ECG) or navigator gating are used to minimize the shot-to-shot variation. Diffusion imaging represents perhaps the extreme case. Because the sequence is sensitized to diffusion, it is extremely sensitive to any minute motion on the subvoxel level that varies over time. As a result, the data acquired by each shot are corrupted to a different extent each time, resulting in image artifacts. This complication has led to the dominance of single-shot techniques for diffusion imaging (24). In recent years, with more in-depth understanding of how to deal with the shot-to-shot variations in diffusion imaging and more sophisticated reconstruction algorithms, new multi-shot diffusion imaging techniques have been developed, which led to a substantial improvement in image resolution and quality (25,27 29) (Fig. 12).

10 Ultrafast Imaging 261 Figure 12. Comparison of the level of distortion in the human brain at the level of the eye and cerebellum, acquired with (from left to right) fast spin echo (FSE) as an anatomical reference, EPI (no parallel imaging, scan time of 29 s), EPI with three-fold acceleration by GRAPPA parallel imaging (scan time of 1 min 40 s), and readout-segmented (RS)-EPI with threefold GRAPPA acceleration and different blind widths (W ¼ 64, 5 blinds, scan time of 4 min 30 s or W ¼ 32, 9 blinds, scan time of 5 min 34 s). To better appreciate the extent of geometric distortions among the acquisitions, anatomical contours outlined in the FSE scan were drawn in white on top of the EPI scans to allow a pixel-wise comparison of the geometry. The corresponding k-space trajectories are shown on the bottom row for the EPI scans. Single-shot EPI reads out the entire k-space in one shot, leading to a long readout time, a large echo spacing (i.e., long time separation between successive lines in the EPI train, or low pseudo-bandwidth in the phase-encoding direction), and hence a high level of distortion. With parallel imaging, the echo spacing is shortened, in this example by three-fold, thereby reducing the distortion. With multi-shot RS-EPI, the echo spacing is reduced further, thereby further reducing the distortion. The echo spacing, and thus distortion, is reduced with narrower blind width (i.e., smaller W), although more shots are needed to cover k-space. Courtesy of Roland Bammer and Samantha Holdsworth. Tackling Signal Evolution With Parallel Imaging or Other Advanced Reconstruction Techniques Parallel imaging (19 21) is another technique to improve the quality of ultrafast images (77 79). Parallel imaging uses an array of local coils, which provides information about the spatial location of the MR signals. As a result, it is feasible to acquire a sparser version of k-space, which is then converted into a fully acquired k-space through reconstruction. Conceptually, this is akin to acquiring multiple lines of k-space in parallel, thus accelerating the data acquisition process. The improvement in image quality from parallel imaging is analogous to that obtained with the multi-shot approach. Through parallel imaging, one can acquire less data per readout, which is therefore shorter and less susceptible to signal evolution (Fig. 12). At the extreme, using a dense coil array with a large number of elements, one may even replace all the phase-encoding gradients with parallel imaging, in a technique called MR inverse imaging (InI) (80,81). Together with a more sophisticated reconstruction (82), this technique has been applied to functional neuroimaging to assess the BOLD signal with wholehead coverage and an ultrahigh temporal resolution of tens of milliseconds (Fig. 13). In a more common setting, parallel imaging is used to accelerate up to approximately three-fold along each spatial dimension at clinical field strengths of 1.5 Tesla (T) or 3T (83) (Fig. 12). In addition to parallel imaging, recent advances in other reconstruction techniques have opened a new path to ultrafast imaging by taking advantage of the inherent redundancy within the data. These techniques include k-t space Broad-use Linear Acquisition Speed-up Technique (k-t BLAST) (18), HighlY constrained backprojection (HYPR) (84), compressed sensing (85), among others. They enable increased imaging speed by requiring less data to be acquired, and then recovering the missing information during reconstruction. Similar to parallel imaging, the acceleration can be used to benefit ultrafast imaging by shortening the readout. Advanced reconstruction techniques are beyond the scope of this review. Interested readers should refer to ref. (18,84,85). In general, for all acceleration techniques, the gain in acquisition speed can be applied to achieving several benefits simultaneously. For example, in addition to shortening the readout, part of the acceleration can also be used to allow for a longer TR or a lower readout bandwidth, thereby increasing SNR. Tackling Experimental Imperfection With gradient switching rates having reached the safety limit, much of the attention on gradient development has turned to the fidelity of the generated gradient waveform. There has been substantial progress in active shielding in gradients to minimize eddy currents, as well as eddy-current pre-emphasis or

11 262 Tsao Figure 13. (Right) A single-subject 100-ms resolution INI fmri time series of activations to visual stimulation (TR/TE ¼ 100/ 30 ms, flip angle 20, FOV ¼ 200 mm), co-registered to a flattened region of the left occipital cortex. The data were obtained using a 32-channel head coil array at a 3T scanner in 128 randomized trials, each of which consisted of 6 s prestimulus baseline, followed by 8-Hz flashing checkerboard flashing for 0.5 s and subsequently 23.5 s poststimulus (30 s in total for each trial). The time stamps labeled in the figure indicate time after onset of the flashing checkerboard. Courtesy of Fa-Hsuan Lin. compensation, which anticipates the distortion from eddy currents so that the final waveform matches the prescribed one (86). Any residual errors lead to mismapping of data in k-space, and result in image artifacts if they are unaccounted for during the reconstruction process. Thus, fast imaging scans are often preceded by a prescan, which enable the scanner to measure residual deviations in the prescribed k-space trajectory. For example, to correct the Nyquist ghosting in EPI, the common technique is to acquire an additional scan where the phase-encoding gradients are turned off to read the center line of k-space repeatedly (66). By measuring the displacement between each traversal, one can measure and subsequently correct for small timing delays. A variety of techniques have been proposed to map out the actual k-space trajectory (87), which can be incorporated into the reconstruction to eliminate the artifacts. Additional correction can also be performed retrospectively by image analysis (67). Recently, there has been renewed interest in incorporating small physical probes that can be used to track the actual magnetic field gradients that are being generated, and that information can be fed back to the reconstruction to improve image quality (88). Typically, retrospective correction and advanced reconstruction techniques are associated with much higher computation times and have therefore been adopted more slowly into clinical scanners. Recently, most major clinical scanner vendors have revamped their computational architecture to allow for highly parallel computation. This, together with the advances of new-generation graphics cards (89) that provide high computational performance at a low cost, will make retrospective correction and advanced reconstruction techniques much more readily available in the near future. Considerable work has been invested in pulse sequence design to devise techniques that prospectively reduce the effects of concomitant fields. They include gradient separation, quadratic nulling, among others (90). Additional correction of residual effects can be performed by reconstruction (64,65). Because concomitant fields lead to accumulated phase error, it is important to correct them in applications where the signal phase is of primary interest, such as in phase contrast measurements of flow. APPLICATIONS OF ULTRAFAST IMAGING In general, ultrafast imaging requires a more in-depth understanding of artifacts to consciously balance acquisition speed with image quality. Despite the added complexity, ultrafast imaging provides such a dramatic speed advantage that it has found its way into a variety of applications that are infeasible or impractical otherwise with slower techniques. Ultrafast Imaging for Temporal Resolution or Shortened Scan Time Ultrafast imaging is used for freezing physiological motion, capturing dynamic events in real time (Figs. 3, 4), or shortening the total scan time (Figs. 1, 2). The latter may be useful to fit the scan within a breathhold or to allow for a large volume coverage within a reasonable time frame, such as for wholebody scanning (91). In myocardial perfusion imaging, ultrafast imaging is used to observe the first-pass dynamics of the contrast bolus. Typically, perfusion imaging is performed during a breathhold, with ECG triggering. After bolus injection, data are acquired at every diastole to minimize cardiac motion. To achieve a high temporal resolution, it is necessary to acquire as much data as possible during each diastole. The challenge is even greater during a stress test, due to the elevated heart and respiration rates. Ultrafast techniques such as multi-slice gradient-echo EPI (36) have been used for this purpose, although there has been a recent shift toward bssfp (37,92) due to a higher SNR (Fig. 14). The regional function of the myocardium can also be assessed quantitatively in a heartbeat by combining tagging techniques with ultrafast imaging (23,38) (Fig. 4). Other applications include flow assessment (39,93) (Fig. 2), interactive coronary imaging (94) (Fig. 3), among others.

12 Ultrafast Imaging 263 Figure 14. Comparison of three sequences (gradient echo, EPI, and SSFP) for first-pass myocardial perfusion imaging, showing the time frame at baseline (top row) and peak myocardial enhancement (bottom row). All three sequences achieve the same spatial resolution ( mm 3 ). Due to different acquisition efficiencies, they can acquire 3 slices per heart beat, up to a heart rate of 90, 105, and 85 beats per min, respectively. In this example, SSFP yields the best image quality, while EPI can accommodate the highest heart rate. Adapted with permission from ref. (92), originally published by BioMed Central. Courtesy of Eike Nagel. Ultrafast Imaging to Minimize Signal Excitation In addition to fast dynamic changes, there are applications where the magnetization is in a transient state, so it is important to limit the number of excitation pulses to measure this transient properly. For example, this is useful in quantitative T 1 mapping (95,96) using the so-called Look-Locker technique (97), in which the magnetization is inverted using a 180-degree pulse. During the course of T 1 recovery, a small amount of magnetization is excited sequentially to read out the progress of the recovery, which can be fitted to create a parametric map of T 1 values. Another area that is gaining importance is hyperpolarization (98,99), for evaluating metabolism with 13 C-labeled substrates or pulmonary function with noble gases. Hyperpolarization dramatically increases the signals originating from the hyperpolarized substrate by several orders of magnitude. However, the magnetization diminishes with use. Therefore, the number of excitation pulses is usually minimized to prolong the use of the magnetization, and ultrafast imaging readouts are used to acquire as much data as possible after each excitation. Ultrafast Imaging for Applications With Long Preparations or Wait Ultrafast imaging also provides substantial utility in applications that take significant time to set up the image contrast or to wait for the appropriate moment to image. In those applications, it is important to acquire as much data as possible in each repetition to shorten the overall scan duration. An example is in functional MRI studies. To generate a high blood-oxygenation-level-dependent (BOLD) contrast to detect the hemodynamic response, it is necessary to have a long echo time, but this also reduces the scan efficiency. Therefore, to achieve whole-head coverage, BOLD imaging is typically performed with either EPI (100) or spiral scans (34) to maximize the data acquisition per repetition. Diffusion imaging is another application where the Stejskal-Tanner diffusion-sensitizing module (101) of the pulse sequence takes considerable time to reach a sufficiently high b factor. As a result, ultrafast imaging helps to shorten scan time. Moreover, due to the shot-to-shot variation mentioned before, singleshot imaging has been instrumental in widening the practical use of diffusion imaging (24), until the more recent development of high quality multi-shot techniques (25,27 29) (Fig. 12). Similarly, ultrafast imaging is useful in free-breathing high-resolution coronary imaging, because considerable amount of time is spent waiting for diastole and end-expiration to minimize motion (Fig. 1). Both EPI and spiral trajectories are used for this purpose (8,102,103). Arterial spin labeling (104) also benefits from ultrafast imaging. Arterial spin labeling is used for quantitative measurement of perfusion by tagging the magnetization of inflowing blood. This is followed by a delay to allow the tagged blood to flow into the slice being measured. Images are acquired with and without tagged blood, and their difference is used to quantify the perfusion. Due to the wait for the transit of blood and the desire for a large volume coverage, ultrafast imaging is useful for shortening the overall scan duration. SUMMARY In ultrafast imaging, acquisition speed is gained by making the pulse sequence as efficient as possible. Conventionally, the main readout techniques for ultrafast imaging are EPI and spiral imaging. Both techniques achieve faster imaging speed by reducing idle time in the pulse sequence, and increasing the readout window to use more of the repetition time for data acquisition. In doing so, they also open up more time for artifacts to contaminate the data. As a result,

13 264 Tsao there is an inevitable trade-off between acquisition speed and the sensitivity to artifacts. The appearance of artifacts in EPI and spiral imaging is quite different, which is due to how data from different times are gathered in the data matrix. In EPI where data are gathered in a zig zag manner through the data matrix, artifacts appear as geometric distortions, signal voids, and Nyquist ghosting. In spiral, where data are gathered in a concentric manner, artifacts appear as blurring, signal voids, and magnification ghosts. In general, these artifacts can be reduced significantly by shortening the readout window, such as by limiting the matrix size, or increasing the number of shots. The latter gain can also be achieved with parallel imaging, and other advanced reconstruction techniques. Moreover, over the past couple of decades, there has been significant progress in artifact reduction, either by prospective adjustments or by retrospective corrections, which has allowed robust ultrafast imaging to be applicable on a routine basis. k-space (46,47) is a graphical representation of an image in terms of its spatial frequencies. Spatial frequencies are complex-valued sinusoidal patterns of pixel intensities that vary across the field of view. The central part of k-space indicates the low frequencies (i.e., slowly varying intensities across the image), while the periphery indicates the high frequencies (i.e., fast varying intensities across the image). Each point in k-space corresponds to a given spatial frequency, and the intensity (magnitude and phase) of that point signifies the magnitude and phase of that sinusoidal function. If one multiplies the sinusoidal function by its magnitude and phase, repeat for all positions in k-space, and add up these scaled sinusoidal functions, one obtains the image (Fig. 15). This is in essence the process of the inverse Fourier transform. All images can be represented in this manner as a sum of scaled sinusoidal functions. In typical images, k-space is much brighter in the center, and it decays rapidly toward the periphery, indicating that most of the signals are contained in the slow-varying spatial frequencies. ACKNOWLEDGMENTS I thank Michael S. Hansen for valuable input; Roland Bammer, Fa-Hsuan Lin, Eike Nagel, Krishna Nayak, Nael Osman, and Matthias Stuber for providing materials for figures; and Frank Korosec, Joseph C. McGowan, and Marcus Alley for their invitation to participate in the ISMRM course. There were many others who contributed materials to the lecture slides, which could not be included due to space limitations. Thank you. APPENDIX k-space Figure 15. The k-space (left) is a graphical representation of the spatial frequency coefficients that make up an image. Each point in k-space corresponds to a distinct spatial frequency pattern, with the central portion of k-space representing the lower frequencies, and the periphery representing the higher frequencies. Each point in k-space carries a complex-valued coefficient, and the brightness represents the magnitude of this coefficient. Reconstruction essentially amounts to multiplying the complex-valued coefficient at each k-space location with the corresponding spatial frequency, and summing across all k-space locations to yield the reconstructed image (right). REFERENCES 1. Cohen MS, Weisskoff RM. Ultra-fast imaging. Magn Reson Imaging 1991;9: Stehling MK, Charnley RM, Blamire AM, et al. Ultrafast magnetic resonance scanning of the liver with echo-planar imaging. Br J Radiol 1990;63: Mansfield P. Real-time echo-planar imaging by NMR. 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