Zigzag Sampling for Improved Parallel Imaging

Transcription

1 Magnetic Resonance in Medicine 60: (2008) Zigzag Sampling for Improved Parallel Imaging Felix A. Breuer, 1 * Hisamoto Moriguchi, 2 Nicole Seiberlich, 3 Martin Blaimer, 1 Peter M. Jakob, 1,3 Jeffrey L. Duerk, 4 and Mark A. Griswold 4 Conventional Cartesian parallel MRI methods are limited to the sensitivity variations provided by the underlying receiver coil array in the dimension in which the data reduction is carried out, namely, the phase-encoding directions. However, in this work an acquisition strategy is presented that takes advantage of sensitivity variations in the readout direction, thus improving the parallel imaging reconstruction process. This is achieved by employing rapidly oscillating phaseencoding gradients during the actual readout. The benefit of this approach is demonstrated in vivo using various zigzagshaped gradient trajectory designs. It is shown that zigzag type sampling, in analogy to CAIPIRINHA, modifies the appearance of aliasing in 2D and 3D imaging, thereby utilizing additional sensitivity variations in the readout direction directly resulting in improved parallel imaging reconstruction performance. Magn Reson Med 60: , Wiley-Liss, Inc. Key words: zigzag sampling; parallel imaging; MRI; GRAPPA; CAIPIRINHA THEORY In recent years, parallel imaging techniques have been In order to demonstrate the effect of zigzag readout trajectories on the aliasing appearance in the image domain, a shown as an elegant way to reduce the scan time of MRI experiments. Parallel imaging takes advantage of the varying spatial sensitivity information of a receiver coil array conventional 4-fold accelerated acquisition is schematically displayed in Fig. 1a. Standard Cartesian data undersampling in the phase-encoding direction corresponds to a to partially accomplish spatial encoding in addition to phase encoding with magnetic field gradients (1 3). Thus, reduced field of view (FOV) in the phase-encoding direction, thereby yielding the well-known aliasing artifacts a successful parallel MRI (pmri) reconstruction strongly that occur only in the phase-encoding directions. By applying rapidly oscillating phase-encoding gradients during depends on the sensitivity variations provided by the receiver array in the directions in which the data reduction the readout process (Fig. 1b, left), sampling positions can and accordingly the phase encoding is carried out. be shifted in the phase-encoding direction in an oscillating Today, modern MR scanners from various manufacturers provide up to 32 independent receiver channels that fashion (Fig. 1b, middle). In this schematic the sampling points along the readout k-space trajectory are positioned allow simultaneous signal reception with large receiver on a Cartesian grid. After inverse Fourier transformation coil arrays. The surface coils within the array are usually the modified aliasing conditions can be clearly seen (Fig. positioned such that the object under investigation is covered from many different angles. Thus, these coil arrays 1b, right). In addition to the fold-over artifacts in the phase-encoding direction (k y ), aliasing in the readout (k x ) usually provide sensitivity variations in all three spatial direction can be observed. dimensions, which generally allows for a high flexibility In previous work it was shown that undersampling in in parallel imaging, because arbitrary slice positions and two directions results in improved aliasing conditions, orientations in combination with highly accelerated par- and therefore in better pmri reconstruction quality (5). Recently, CAIPIRINHA was presented, which additionally modifies the aliasing conditions in two dimensions in 1 Research Center Magnetic-Resonance-Bavaria, Würzburg, Germany. such a way that further improved reconstruction quality is 2 Department of Radiology, Tokai University, Isehara, Japan. achieved (4). However, both concepts are limited to 3D 3 Department of Experimental Physics 5, University of Würzburg, Würzburg, imaging, as undersampling is carried out only in the Germany. 4 Department of Radiology, University Hospitals of Cleveland and Case Western Reserve University, Cleveland, Ohio. sampling along a zigzag gradient trajectory allows for un- phase-encoding directions (k y,k z ). Figure 1 indicates that Grant sponsor: German Research Society (Deutsche Forschungsgemeinschaft, dersampling in the read direction (k x ) as well. Thus, the 2D DFG); Grant number: JA 827/4-4; Grant sponsor: Siemens Medical CAIPIRINHA concept can be applied to 2D imaging as Solutions. *Correspondence to: Dr. Felix Breuer, Research Center, Magnetic Resonance well. The logical extension to 3D CAIPIRINHA can be Bavaria, Am Hubland, Würzburg, Germany. breuer@mr-bavaria.de performed using the zigzag trajectory for 3D imaging. The sampling patterns achievable with zigzag readouts Received 11 September 2007; revised 28 January 2008; accepted 12 March strongly depend on the gradient performance and are limited by potential neurostimulations caused by rapidly DOI /mrm Published online in Wiley InterScience ( changing magnetic fields. While conventional Cartesian 2008 Wiley-Liss, Inc. 474 allel imaging are feasible. However, in conventional Cartesian pmri sensitivity variations can only be exploited in the phase-encoding directions. While the CAIPIRINHA strategy has been shown to employ the sensitivity variations most efficiently in these dimensions (4), the sensitivity variations available in the readout direction remain unused in any Cartesian pmri reconstruction method. Thus, in this work it will be shown that by additionally switching rapidly oscillating magnetic field gradients in the phase-encoding directions during the readout, sensitivity variations in the readout direction can be employed in the parallel imaging reconstruction procedure. This use of additional sensitivity variations results in a significantly improved image quality, with less noise enhancement and a more homogeneous noise distribution compared to conventional Cartesian pmri methods.

2 Zigzag Sampling for Improved Parallel Imaging 475 FIG. 1. Schematic description of (a) a conventional R 4 accelerated MRI pulse sequence (left) with straight readout lines (middle) resulting in aliasing only in the phase-encoding direction (right). b: Identical experiment with an additional zigzag-shaped phase-encoding gradient switched during the readout process (left) resulting in oscillating readout k-space trajectories (middle) and aliasing in both the phaseencoding and the read direction (right). data reduction by a factor of R results in exactly R aliased image pixels to be unfolded, the zigzag sampling strategy can result in many more image pixels aliased on top of each other. These image pixels are differently weighted as a result of the nonuniformly distributed point spread function. While this fact must be considered in SENSE reconstructions, for example, using the conjugate gradient SENSE approach (6,7), conventional GRAPPA with multiple reconstruction blocks can also be employed in such a situation (8,9). MATERIALS AND METHODS In vivo head experiments were performed on a 1.5T clinical scanner (Siemens Avanto, Erlangen, Germany) equipped with a gradient system allowing for maximum slew rate of 125T/m/s and maximum gradient amplitude of 33mT/m. For data reception the standard Siemens 12- channel head coil array was used, which is composed of two six-element rings in axial direction. A standard FLASH sequence (field of view [FOV] mm 2, matrix , bandwidth [BW] 195 Hz/pixel, 30, slice thickness 8 mm) was modified by applying a rapidly oscillating zigzag-shaped gradient along the phaseencoding axis in addition to the conventional readout gradient. This additional gradient results in data sampled along an oscillating readout trajectory instead of a conventional straight readout line. Fully encoded datasets were acquired with different zigzag-shaped gradients played out during readout. The gradient trajectories were designed to have a different number of oscillations. In addition, the gradient strength was increased until the maximum tolerable gradient amplitude was reached. Examples of the measured trajectories with 32 and 16 oscillations are given in Ref. (7). Even high-performance gradient systems can perform only marginal shifts in k-space when the gradient is switched on and off between two subsequent readout points. In order to travel farther in k-space, the gradients need more time to achieve larger shifts in k-space. Therefore, gradient trajectories with fewer oscillations must be used in order to have a significant effect on the parallel imaging reconstruction performance. In this work, experiments were performed employing gradient trajectories with 64, 32, 21, 16, and 8 oscillations. In order to mimic accelerated zigzag sampled pmri acquisitions, phase-encoding steps were retrospectively removed from the fully encoded zigzag datasets. The in vivo head datasets were generated with healthy volunteers, and informed consent was obtained prior to the acquisition. All image reconstructions were performed offline using the MatLab programming environment (MathWorks, Natick, MA). Specialized image reconstruction was performed in two separate steps, namely, the initial parallel imaging reconstruction process (zigzag GRAPPA) followed by the gridding procedure. For both actions the exact knowledge of the zigzag k-space trajectory employed is required. In order to obtain this information trajectory measurements were carried out using the method proposed by Duyn et al. (10). Zigzag GRAPPA In contrast to conventional Cartesian GRAPPA, where only one GRAPPA reconstruction block is needed (3,11) to calculate all the missing points in the undersampled dataset, multiple GRAPPA reconstruction blocks are required for a successful parallel imaging reconstruction in datasets sampled along a zigzag trajectory. In Fig. 2a a typical Cartesian

3 476 Breuer et al. linearly increasing phase in the y direction (image space in y). In order to shift the points sampled along a zigzag trajectory onto a straight line, knowledge of the oscillating trajectory allows for the calculation of the phase needed to shift each k x position (see Fig. 3). FIG. 2. a: A single 5 2 reconstruction block is needed for GRAPPA reconstruction of an accelerated experiment sampled along a straight readout line. b: Multiple 5 2 reconstruction blocks are needed for GRAPPA reconstruction of an accelerated experiment sampled along an oscillating readout trajectory. In this schematic the black points represent the source points in all coils (coil dimension not shown) and the white points the target points in one coil. GRAPPA reconstruction block for a reduction factor of R 3 including five source points in the k x direction is depicted. In order to demonstrate the need for multiple GRAPPA kernels in accelerated datasets sampled along a zigzag trajectory, Fig. 2b schematically displays four different GRAPPA kernels along the readout direction. The number of reconstruction kernels needed depends on how many k-space points are acquired during one zigzag cycle. For example, a k-space trajectory with 256 readout points sampled along a gradient trajectory with 32 cycles requires 8 different reconstruction kernels. Either a fully encoded low-resolution Cartesian or zigzag reference scan can be employed as the autocalibration signal (ACS) for the GRAPPA reconstructions. Data sampled along zigzag trajectories normally do not fall on a Cartesian grid in the k y direction, which means that a standard ACS dataset will not contain the necessary source points to determine the necessary GRAPPA weights. Thus, in order to obtain the weights the ACS dataset (size: 32 32) was Fourier interpolated to 16-times its original size in the k y direction. GRAPPA weights for a specific zigzag pattern can then be calculated by selecting the source and target points in the oversampled k-space which correspond most closely to the non-cartesian zigzag data. Interpolation onto a 16- times finer grid has shown to be sufficient and further interpolation did not result in improved reconstruction quality. The interpolation procedure could also be performed using the Fourier Shift Theorem. Zigzag Data Gridding After zigzag GRAPPA reconstruction a fully encoded zigzag dataset is obtained. Using the knowledge of the zigzag k-space trajectory, the sampled points can be gridded onto a Cartesian grid by using the well-known Fourier Shift Theorem. Because the zigzag data are purely Cartesian in the k y direction, all the data points along k y (at a certain k x position) can be shifted in the k y direction by applying a Zigzag Data Simulation Finally, the concept of zigzag sampling was applied to volumetric parallel imaging. For demonstration purposes, a zigzag-type 3D acquisition was simulated from a fully encoded conventional 3D head MPRAGE experiment performed on the Avanto system (FOV , matrix , TE/TR 3.1 ms/1900 ms, TI 1100 ms, BW 130 Hz/pixel) with the 12-channel head coil described earlier. Using a procedure similar to the gridding method described above, one can simulate data along a zigzag trajectory by shifting the Cartesian points to a computed or measured zigzag k-space trajectory by taking advantage of the Fourier Shift Theorem. Similar to the 2D case, accelerated zigzag-sampled pmri 3D acquisitions were mimicked by retrospectively removing phase-encoding steps from the fully encoded simulated zigzag datasets. The final reconstruction procedure was performed in analogy to the 2D zigzag reconstruction process, however, extended to an additional spatial dimension (11,12). A fully encoded low-resolution dataset (matrix size ) in the center of k-space served as ACS for the GRAPPA weights determination. The size of the reconstruction kernels was chosen to be RESULTS In preliminary experiments several different k-space trajectories were investigated using different zigzag gradient FIG. 3. Zigzag-shaped readout gradient trajectory with 16 oscillations applied in the y direction (top) and corresponding measured k-space trajectory (bottom). The amplitude of the k-space trajectory is given by the integral covered by the gradient and thus can be adjusted by either changing the gradient strength or using fewer oscillations. Fully encoded zigzag data can be shifted back onto a straight line by applying a linearly increasing phase (exp( i k y y)) in the y direction (image domain) according to the distance from a straight line ( k y ) for each k x position.

4 Zigzag Sampling for Improved Parallel Imaging 477 FIG. 4. a: Unaccelerated (R 1) reference image. R 4 GRAPPA reconstructions after (b) conventional sampling without zigzag and (c) with an additional zigzag shaped gradient applied in the phaseencoding direction. The zigzag gradient trajectory was designed to have 16 oscillations and a maximum shift of sampling positions of 2.5 k y at an FOV 16.5 cm. designs. It has been observed that when the oscillating gradient is switched more rapidly, the maximum possible amplitude that can be reached by the k-space trajectory is smaller. The image quality after zigzag GRAPPA reconstruction significantly improved with fewer oscillations, which is equivalent to covering larger areas of k-space with each oscillation. Based on these findings, the gradient used in the following experiment consisted of 16 oscillations along the readout trajectory. The measured k-space trajectory is depicted in Fig. 3. The amplitude of the k- space trajectory achieved with our gradient system at an FOV of 165 mm in the phase-encoding direction was 2.5 k y.r 4 times accelerated experiments were then performed without and with this zigzag trajectory. In Fig. 4 the image reconstruction results are shown after conventional Cartesian GRAPPA (middle) and zigzag GRAPPA (right). In addition, the unaccelerated (R 1) experiment is shown (left) as a reference. In addition, to demonstrate that the zigzag concept is not limited to 2D imaging, reconstruction results using two different R 6-fold accelerated 3D acquisition strategies are shown in Fig. 5 after conventional (R 2 3) data reduction without (Fig. 5a) and with an additional zigzag gradient switched along the phase-encoding direction (Fig. 5b). In order to demonstrate the effect of the zigzag concept on the entire 3D volume, images are presented in the sagittal, axial, and coronal view for each case. DISCUSSION In this article, zigzag sampling, which enables a more efficient exploitation of the sensitivity variations provided by the underlying receiver coil array in the imaging plane (volume), has been described. As schematically depicted in Fig. 1b, data points sampled along a zigzag trajectory result in aliasing artifacts that appear not only in the phase-encoding direction but also in the readout direction. Thus, zigzag sampling in 2D imaging shows aliasing patterns similar to those known from 2D SENSE or 2D CAIPIRINHA-type acquisitions used in accelerated 3D imaging, and therefore shares the same advantages. However, Fig. 1b gives only an idea of how aliasing appears in zigzag sampling. Theoretically, the optimal pattern for parallel imaging performance would be to shift every second readout point by R/2 k y. However, it is clear that such sampling is not possible with current gradient systems, and even if such gradient systems were available, one could not use the sequence on a patient because of potential neurostimulations. Since current high-performance gradient systems can only shift every second readout point by less than 0.1 k y in the phase-encoding direction (which has basically no effect on the parallel imaging performance), fewer oscillations must be used in order to provide larger shifts in the phase-encoding direction between subsequent readout points. In this work, various gradient trajectories were implemented providing 64, 32, 21, 16, and 8 oscillations. The trajectory with 16 oscillations was found to be optimal. However, in future work strategies must be found to determine the optimal gradient trajectory given a certain imaging sequence, reduction factor, gradient performance, and receiver coil. However, using zigzag trajectories, sensitivity variations can be utilized in two (instead of one) spatial dimensions in conventional single-slice imaging and in all three dimensions (instead of two) in volumetric parallel imaging. A successful parallel imaging reconstruction process strongly depends on sufficient sensitivity variations, especially at high acceleration rates. Both the 2D and 3D experiments presented here demonstrate that sensitivity variations in the read-direction have been additionally utilized. Thus, the zigzag sampling strategy resulted in significantly improved reconstruction performance, thereby allowing for higher image acceleration. The zigzag-type sampled experiments shown here share the same number of excitations (phase-encoding steps) and readout samples as the conventional imaging strategy using a straight readout trajectory, and therefore both have the same SNR without parallel imaging. Additionally, the image contrast is maintained, which makes this concept easily applicable to many clinical pmri protocols. It is important to note that the expected improvement in reconstruction quality due to zigzag sampling strongly depends on the reduction factor and the encoding capacity of the receiver array. In imaging situations with moderate accel- FIG. 5. Sagittal, axial, and coronal views of R 6-fold accelerated 3D experiments using (top row) conventional rectangular data reduction without zigzag sampling and (bottom row) rectangular data reduction with zigzag sampling.

5 478 Breuer et al. erations where conventional GRAPPA already provides high reconstruction quality (low g-factor), the effect of zigzag sampling has only a small effect. In contrast, highly accelerated imaging at the limit of the coil encoding capacity in only one direction (high g-factor) will greatly benefit from the zigzag approach. As the zigzag sampled k-space is still Cartesian in k y for every k x position, a very fast and simple gridding strategy can be used and no special algorithms are required. Although non-cartesian parallel imaging strategies are also capable of taking advantage of the sensitivity variations in all dimensions (e.g., radial, spiral) these methods often require extensive gridding algorithms and nontrivial pmri reconstruction procedures (13 15). The accelerated 3D zigzag experiment, for simplicity purposes only, was confined to a standard rectangular (e.g., R 2 3) data reduction in the phase-encoding directions in combination with a zigzag trajectory applied only in one phase-encoding direction. Another option would be to employ an optimized 2D CAIPIRINHA phaseencoding pattern in combination with two zigzag gradient trajectories applied in both phase-encoding directions. This strategy could further improve the parallel imaging reconstruction results. It is anticipated that faster gradient systems will allow for further improved parallel imaging performance. However, this type of zigzag sampling requires rapidly switched gradients and therefore may potentially cause peripheral neurostimulations. Thus, this trajectory is limited to sequences with moderate acquisition bandwidths. However, in many clinically relevant sequence protocols the acquisition bandwidth is chosen to be rather low to provide sufficient signal-to-noise ratio (SNR) in the final image. However, in some cases it could be beneficial to further decrease the acquisition bandwidth in order to take advantage of both the improved parallel imaging reconstruction due to zigzag sampling and the increased base SNR due to the lower acquisition bandwidth, although some signal loss due to prolonged echo times would be expected. CONCLUSION In all currently available Cartesian pmri methods, potential sensitivity variations in the readout direction have not been employed in the parallel imaging reconstruction process. In this work, a new concept has been presented that allows for significantly improved parallel imaging by simply replacing the straight readout line in conventional Cartesian pmri with an oscillating readout trajectory. It has been shown that sensitivity variations available in the read direction can be additionally exploited in the pmri reconstruction process, resulting in significantly improved reconstruction quality. Such k-space trajectories can be easily accomplished by switching zigzag-shaped gradients in the phase-encoding direction during the readout, and therefore can be directly implemented in many clinical protocols. As shown in this work, this type of sampling is applicable to both single-slice (2D CAIPIRINHA) and volumetric parallel imaging (3D CAIPIRINHA) and in both cases yields significantly improved image quality. REFERENCES 1. Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med 1997;38: Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42: Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002;47: Breuer FA, Blaimer M, Mueller MF, Seiberlich N, Heidemann RM, Griswold MA, Jakob PM. Controlled aliasing in volumetric parallel imaging (2D CAIPIRINHA). Magn Reson Med 2006 Mar;55: Weiger M, Pruessmann KP, Boesiger P. 2D SENSE for faster 3D MRI. MAGMA 2002;14: Pruessmann KP, Weiger M, Boernert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med 2001;46: Breuer F, Moriguchi H, Seiberlich N, Blaimer M, Duerk J, Jakob P, Griswold M. Zigzag sampling for improved parallel imaging. In: Proc ESMRMB 23, Warsaw, Poland; 2006, # Griswold MA, Heidemann RM, Jakob PM. Direct parallel imaging reconstruction of radially sampled data using GRAPPA with relative shifts. In: Proc ISMRM 11; p Seiberlich N, Heidemann RM, Breuer FA, Blaimer M, Griswold MA, Jakob PM. Pseudo-Cartesian GRAPPA reconstruction of undersampled non-cartesian data. In: Proc ISMRM 14; p Duyn JH, Yang Y, Frank JA, van der Veen JW. Simple correction method for k-space trajectory deviations in MRI. J Magn Reson 1998; 132: Breuer FA, Blaimer M, Seiberlich N, Griswold M, Jakob PM. A 3D GRAPPA algorithm for volumetric parallel imaging. In: Proc ISMRM 14; p Blaimer M, Breuer FA, Mueller M, Seiberlich N, Ebel D, Heidemann RM, Griswold MA, Jakob PM. 2D-GRAPPA-operator for faster 3D parallel MRI. Magn Reson Med 2006;56: Heidemann RM, Griswold MA, Seiberlich N, Kruger G, Kannengiesser SA, Kiefer B, Wiggins G, Wald LL, Jakob PM. Direct parallel image reconstructions for spiral trajectories using GRAPPA. Magn Reson Med 2006;56: Heberlein K, Hu X. Auto-calibrated parallel spiral imaging. Magn Reson Med 2006;55: Yeh EN, Stuber M, McKensie CA, Botnar RN, Leiner T, Ohliger MA, Grant AK, Willig-Onwuachi JD, Sodickson DK. Inherently self-calibrating non-cartesian parallel imaging. Magn Reson Med 2005;54:1 8.