EPI Nyquist Ghost and Geometric Distortion Correction by Two-Frame Phase Labeling

Transcription

1 FULL PAPER Magnetic Resonance in Medicine 00:00 00 (2016) EPI Nyquist Ghost and Geometric Distortion Correction by Two-Frame Phase Labeling Victor B. Xie, 1,2 Mengye Lyu, 1,2 and Ed X. Wu 1,2 * Purpose: To develop a new Nyquist ghost and geometric distortion correction method in echo planar imaging (EPI) using parallel imaging. Methods: Two frames of EPI data are acquired with normal and phase-labeled sequence. The phase label is applied by modifying the PE prephase gradient to shift the central echo by one echo spacing. GRAPPA weights are trained from both frames and used to reconstruct images from positive or negative echoes in each frame to remove Nyquist ghost. Geometric distortion is then corrected by the B 0 field map generated from the phase difference between positive and negative echo images. Phantom and in vivo experiments at 7 Tesla (T) and 3T were performed to evaluate the proposed method. Results: Nyquist ghost was greatly reduced in all images even under oblique imaging and poor eddy current conditions, yielding significant improvements over the existing reference scan and image entropy minimization based methods. Image geometries were fully restored after distortion correction. Phantom results indicated that the signal-to-noise ratio efficiency was largely preserved while fmri results showed no apparent degradation of temporal resolution. Conclusion: The proposed method provides robust correction of both Nyquist ghost and geometric distortion in EPI, and it is particularly suitable for dynamic EPI applications. Magn Reson Med 000: , VC 2016 Wiley Periodicals, Inc. Key words: EPI artifacts; Nyquist ghost correction; geometric distortion correction; parallel imaging; fmri INTRODUCTION Echo planar imaging (1) has been widely applied in various MRI applications, such as functional MRI (fmri) and dynamic susceptibility contrast-enhanced (DSC) imaging, because of its fast imaging capability. However, echo planar imaging (EPI) image quality is intrinsically hindered by two major artifacts, i.e., Nyquist ghost and geometric distortion. 1 Laboratory of Biomedical Imaging and Signal Processing, The University of Hong Kong, Pokfulam, Hong Kong SAR, China. 2 Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong SAR, China. Grant sponsor: Hong Kong Research Grant Council; Grant number: GRF HKU ; Grant sponsor: HKU matching fund for the State Key Laboratory of Pharmaceutical Biotechnology. *Correspondence to: Ed X. Wu, Ph.D., Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong SAR, China. ewu@eee.hku.hk Received 16 October 2015; revised 3 March 2016; accepted 30 March 2016 DOI /mrm Published online 00 Month 2016 in Wiley Online Library (wileyonlinelibrary. com). VC 2016 Wiley Periodicals, Inc. 1 To shorten the acquisition time, EPI usually acquires data in both positive and negative readout polarities. Thus, any imperfections in the gradient system, such as eddy current and time delay, lead to a signal modulation with half the Nyquist frequency in k-space, producing a ghost in image space, which is the object shifted by half of the field of view (FOV) along the phase encoding (PE) direction and often called Nyquist ghost or N/2 ghost. Numerous methods have been proposed to correct Nyquist ghost. In general, these methods can be divided into two groups based on whether the phase error is corrected using a model or not. The first group consists of model-based correction methods, in which the phase error is usually modeled as one-dimensional (1D) linear phase error (2,3), 1D nonlinear phase error (4), or 2D phase errors (5 7) in projection x-k y space. Phase error can be estimated and modeled from a reference scan (2,4) or image based entropy optimization (3). However, these models are not precise because eddy current and magnetic susceptibility effect can introduce high-order phase errors, especially in oblique imaging where different physical gradient may have different eddy current and time delay (8,9). The other group is interleaved data methods, which include the resampling of the same k-space with opposite readout polarity either in the same scan (10) or temporally interleaved scans (11). Nyquist ghost is eliminated by realigning k-space with positive or negative echoes (i.e., echoes sampled on positive or negative readout) to avoid any phase inconsistency between them. Such interleaved data methods suffer from long echo train length or low temporal resolution because the k-space needs to be sampled twice in opposite polarities. With the invention of parallel imaging (12,13), several new methods have been proposed. EPI k-space data are separated into two groups of positive or negative echoes. Each echo group is equally undersampled by a factor of two and can be reconstructed into a Nyquist ghost free image using parallel imaging reconstruction methods (14 17). The other major EPI image artifact is the geometric distortion caused by field inhomogeneities, which often stem from imperfect shimming and local tissue/air magnetic susceptibility. The erroneous phase of offresonance spins accumulates in the acquisition window or echo train. It results in signal mismapping and image geometric distortion. Geometric distortion occurs most prominently along PE direction because of the low PE sampling bandwidth associated with the relatively long echo spacing. Improvements in shimming hardware have enabled the reduction of field inhomogeneities and reduced such image distortion. Parallel imaging can

2 2 Xie et al. FIG. 1. Illustration of the proposed two-frame EPI sequence for gradient echo EPI. The first frame is a normal single-shot EPI (ss- EPI). The second frame is phase labeled by subtracting an area equal to one PE blip from the PE prephase gradient. This phase label shifts the k-space acquisition grid up by one line along k y, and increases TE by one echo spacing. This two-frame acquisition provides full k-space lines sampled with both positive and negative readout polarities. shorten the acquisition window by undersampling, increase the effective PE sampling bandwidth, and lead to significant image distortion reduction by the acceleration factor (12,13). Such parallel imaging can reduce distortion but cannot correct it fully. Meanwhile, various distortion correction methods have been proposed. In general, these methods involve two steps. First, information about field inhomogeneities in the form of field map, point spread function, or pixel shift map is acquired through single or multiple scans with different parameters, such as the echo time (TE) (18,19), the location of k-space data (20,21), and the polarity of the PE (22,23). Then geometric distortion is removed by modulating the frequency components in k- space or unwrapping image by resampling and linearly interpolating in the image domain. Because information about field inhomogeneities is usually acquired in a separate reference scan, it is imperative that the B 0 field remains the same in both measurements. However, during lengthy or repeated measurement such as fmri and DSC imaging, magnetic field may not usually be constant because physiological fluctuation and motion are often present (24), and it is impractical to insert scans to map the B 0 field during these dynamic scans. Two artifacts described above greatly limit the EPI image quality. So far, only very few methods can potentially deal with both artifacts together (25,26). Among these methods, phase labeling for additional coordinate encoding (PLACE) is relatively effective at the cost of reduced temporal resolution (26). In PLACE, images are phase labeled by varying the area of the PE prephase gradient to shift the acquired k-space grid. When a shift of one echo spacing is applied to the second frame, each phase-encoded line in k-space is acquired in the opposite readout polarity. Nyquist ghost is effectively eliminated by averaging the two complex images after removing the linear phase ramp introduced by phase labeling, due to the cancellation of the phase errors, including high-order phase errors, in echoes sampled in positive and negative readout. Phase labeling also encodes the undistorted original y- coordinate of each pixel into the phase difference between two images with different phase labels. A pixel shift map can be generated from the phase difference map and used to correct distortion in the image domain. PLACE can correct either Nyquist ghost or geometric distortion using two frames. Because only one Nyquist ghost corrected image is generated from the combination of two frames, three frames [with three phase labels by varying PE prephase gradient, and thus three echo times (TEs)] have to be acquired to correct both artifacts. Two Nyquist ghost corrected images are generated from the combination of the first two and last two frames, respectively. Geometric distortion in these two images is then corrected using the pixel shift map generated from the phase difference of these two images. Such PLACE approach reduces the temporal resolution, limiting its performance in dynamic EPI applications where temporal information is crucial. Here, we develop a new approach to correct both Nyquist ghost and geometric distortion in EPI without compromising temporal resolution by using parallel imaging. Instead of treating the Nyquist ghost free image (formed from the summation of the two complex images reconstructed from two frames) as the final single image as in PLACE, our proposed method uses the composite k- space data to train GRAPPA weights. Four Nyquist ghost free images are then reconstructed from the positive or negative echoes in two frames. These images largely preserve the temporal resolution. They also retain the phase information for subsequent geometric distortion correction. As a result, two Nyquist ghost and distortion corrected images can be obtained for two respective frames, and they can be combined if necessary. In the following, we first explain the principle of this method, then demonstrate its feasibility and utility under practical EPI conditions by phantom and in vivo experiments. METHODS Pulse Sequence In the proposed method, the modified sequence consists of two frames; one is normal single-shot EPI (ss-epi), the other one is phase labeled ss-epi, as illustrated in Figure 1 for gradient echo (GE) EPI. In the phase labeled frame, an area equal to one PE blip is subtracted from PE prephase gradient. This phase label shifts the k-space acquisition grid up by Dk y from the original grid along PE direction. Each k-space line is sampled in both positive and negative readout polarities in these two frames to correct Nyquist ghost in the reconstruction procedures as described below. It also shifts the TE of the second frame by one echo spacing (Dt y Þ, enabling the B 0 field map calculation and subsequent geometric distortion correction.

3 EPI Ghost and Distortion Correction 3 FIG. 2. Reconstruction procedure for the proposed two-frame EPI acquisition. Multichannel k-space data from two adjacent frames (k 1 and k 2 ) are combined by complex summation and used to train GRAPPA weights. Meanwhile, for each frame, k-space data are separated into two groups by echo polarity. The missing data in each group are synthesized by GRAPPA, yielding two Nyquist ghost corrected images (I p and I n ) from positive and negative echoes, respectively, for each frame. B 0 field map (DB) is generated according to Eq. [1] from four GRAPPA reconstructed images and used for subsequent geometric distortion correction by Eq. [2]. Two corrected images from each frame are averaged to form the final image (I 1 or I 2 ) in dynamic imaging. In static imaging where only one image is needed, I 1 and I 2 can be combined to form one final image I. Image Reconstruction The reconstruction procedure is shown in Figure 2. k 2 is first circular shifted up by one Dk y along PE direction to be aligned with the k-space grid. Multichannel EPI data from two adjacent frames, k 1 and k 2 ; are combined to form one composite k-space dataset by complex summation. The phase errors, including the high-order ones, from positive and negative echoes cancel out. Therefore, this composite k-space dataset is free from Nyquist ghost signal as in PLACE (16,26). In our method, it is used to generate GRAPPA weights (instead of producing a single ghost free image as in PLACE). Meanwhile, data from each frame are grouped into positive and negative echoes. Each group is treated as a k-space undersampled by a factor of two and the missing data can be synthesized by GRAPPA. Thus two Nyquist ghost corrected images (i.e., I p and I n ) are generated from positive and negative echoes, respectively, for each frame. Note that frame k 2 is acquired with phase label compared with frame k 1. Thus the reconstructed images, I 2;p and I 2;n, are also phase labeled compared with I 1;p and I 1;n. This phase label shifts the k-space acquisition grid by Dk y, producing a phase ramp across the image in the range of (-p, p) in PE direction. It also introduces a TE difference between two frames, so B 0 field can be mapped from their phase difference after removing the phase ramp (18,19,27). B 0 field map is calculated as: " DB ¼ Dw ¼ 1 Arg X # I 2;p;l RPR X I 1;p:l þ I 2;n;l RPR I 1;n:l gdt y gdt y l l [1] where Dt y is the TE difference or one echo spacing, l the index of coil channels, I :;:;l: the reconstructed complex image in the l th channel, * the conjugate operation, and ArgðÞthe phase angle of a complex image. In Eq. [1], RP RðÞ is an operation to remove the phase ramp (¼2py=N y ), which is performed in k-space by using a circular shift in PE direction. The phase difference is calculated as the sum of the Hermitian inner products over all channels, so channel-specific phase offsets are automatically removed. Furthermore, the phase in each channel is weighted by the magnitude to effectively suppress noise in the phase image (27,28). Two identical phase differences generated from the two positive and two negative echo images, respectively, are combined to further increase the accuracy. To improve the accuracy and robustness, the B 0 field map is masked based on magnitude image and dilated to remove interference from signal void regions. Then a 2D median filter (kernel size 5 5) is applied to further enhance the accuracy. To reduce ripple artifact, the images are upsampled twice before applying distortion correction by zero-padding in k-space (19). The geometric distortion is first corrected in x-k y space by removing the phase error introduced by field inhomogeneities: 1 Sx; k y ¼ RN y RNy X=2 n¼ RN y =2 jndb x;y Ix; ð yþe ð ÞgDty e j2pky y=rny [2] where Ix; ð yþ is the upsampled image with distortion, R the upsampling factor, N y number of PEs in PE (y) direction, and n the index for N y. Then 1D inverse Fourier transform is applied in PE direction to get a distortion corrected image, which is subsequently downsampled to match the original image size. By modulating the frequency components in the k-space instead of performing a spatial domain shift, not only is the pixel location

4 4 Xie et al. restored but also its intensity corrected. No further intensity correction is necessary; thus, the modulation method is relatively robust to noise or error in the image. After distortion correction, I p and I n for each frame are complex combined to form the final Nyquist ghost free and geometric distortion corrected images (I 1 and I 2 ) for frame k 1 and k 2 in dynamic imaging. For static imaging where only one image is needed, I 1 and I 2 can be further complex combined to form the final image I. Experiments The proposed method was implemented for ss-epi on a 7 Tesla (T) Bruker scanner (70/16 Pharmascan) equipped with a four-channel rat head surface coil and a 3T Philips Achieva scanner equipped with an eight-channel SENSE human head coil. Phantom Experiments To evaluate the Nyquist ghost suppression especially when multiple physical gradients are involved in phase and frequency encoding, GE EPI data of a cylindrical phantom were acquired at 7T in axial, oblique, and double-oblique planes. To further assess the robustness of the proposed method in Nyquist ghost correction in presence of severe eddy current, experiments were performed under different eddy current conditions by changing the time constants and gains of gradient preemphasis unit in three physical axes on the welladjusted 7T Bruker MRI system. Eddy current effect was examined in short (time constant 2 ms and gain 36%) or long (200 ms and 36%) terms separately in readout direction. The combined effect of short (2 ms and 36%) and long (200 ms and 36%) eddy current along PE and slice directions were also examined. For comparison, three Nyquist ghost correction methods, 1D phase correction based on a reference scan (2) (Method R) and image entropy minimization (3) (Method E) and PLACE, were implemented for 7T. Method E and PLACE were implemented for 3T. Methods R and E were used to reconstruct two frames individually. Note that the two-frame phase labeling only enables PLACE to correct Nyquist ghost, but not geometric distortion. Nyquist ghost level was quantitatively evaluated by ghost-tosignal ratio (GSR), which was defined as the ratio of the average signal intensity within a ghost region of interest (ROI) to that within a signal ROI. In this study, the signal ROI was automatically defined by including pixels with signal intensity higher than mean signal intensity of the entire image. The ghost ROI was generated by shifting the signal ROI by half of the FOV along PE direction. To evaluate the distortion correction qualitatively, a structured phantom was imaged at 7T. Before EPI acquisition with the modified sequence, global shimming was performed. GE EPI acquisition parameters for all phantom experiments at 7T were: TE/repetition time (TR) ¼ 25/2000 ms, flip angle ¼ 90, FOV ¼ mm 2, matrix size ¼ , echo spacing ¼ 0.32 ms, and slice thickness ¼ 2 mm. T2 weighted (T2W) images were also acquired with the same geometry as distortion free reference using a rapid acquisition with refocused echoes (RARE) sequence with FOV ¼ mm 2, matrix size ¼ , RARE factor ¼ 8, TE/TR ¼ 36/4200 ms, and average ¼ 2. To quantify the effect of the proposed method on the final image signal-to-noise ratio (SNR) as compared to the entropy method (Method E) and PLACE, 7T and 3T data were acquired on water phantoms. GE EPI parameters for 7T were the same as listed above. For 3T, they were: TE/TR ¼ 30/2000 ms, flip angle ¼ 90, FOV ¼ mm 2, matrix size ¼ 96 96, echo spacing ¼ 0.3 ms, and slice thickness ¼ 4 mm. SNR was measured using the image difference method (29,30). In brief, two sets of magnitude images were reconstructed from two datasets that were consecutively acquired with identical parameters. The signal was defined and measured as the mean signal within a ROI from the sum of these two images, while the noise was measured as the standard deviation of signals within the same ROI in the difference image. In Vivo Experiments In vivo experiments were carried out at 7T and 3T to evaluate the proposed method on animal and human brain imaging. All aspects of the animal experiments were approved by the Committee on the Use of Live Animals in Teaching and Research at the University of Hong Kong. Sprague Dawley (SD) rats were prepared for experiments and scanned at 7T. To test the feasibility of the proposed method, spin echo EPI data were acquired from rat brains using the following parameters: TE/ TR ¼ 46/3000 ms, FOV ¼ mm 2, slice thickness ¼ 4 mm. Other scan parameters were identical to those in the 7T phantom experiments. T2W images were also acquired at the same geometry as reference. Human experiments were performed at 3T with the approval by the Institutional Review Board of the University of Hong Kong. GE EPI data were collected with the following parameters: TE/TR ¼ 30/2000 ms, FOV ¼ mm 2, matrix size ¼ 96 96, slice thickness/gap ¼ 4/2 mm, and number of slices ¼ 15. Other parameters were identical to those in 3T phantom experiments. Volume shimming was performed before each EPI acquisition. For comparison, GE EPI scan was also performed with SENSE factor ¼ 2. 2D T1 weighted (T1W) images were acquired as reference using RARE at the same geometry with TE/TR ¼ 10/450 ms, matrix size ¼ To demonstrate the proposed method for blood oxygenation level dependent (BOLD) fmri at 3T, a fingertapping task was used with a block design paradigm consisting of four blocks of 20 s off and 20 s on. During the on period, the volunteers were instructed to continuously tap the left index finger to the thumb at a selfpaced rate. fmri experiments were conducted using the repeated two-frame single-shot GE EPI sequence with the same 3T parameters as described above. A general linear model analysis was applied to the reconstructed image volume series to calculate the t-value activation maps using SPM8 ( The significantly activated voxels were identified as t > 3.16 (equivalent to P < 0.001, uncorrected) and cluster > 4 in t-value maps.

5 EPI Ghost and Distortion Correction 5 FIG. 3. EPI images of a cylindrical phantom in axial (top), oblique (middle), and double-oblique (bottom) imaging planes at 7T using a four-channel surface RF coil. Each image is displayed with normal and enhanced brightness (6) to visualize the ghost. Each dataset was Nyquist ghost corrected by the 1D phase correction method based on a reference scan (Method R), image entropy minimization method (Method E), PLACE, and the proposed phase labeling method (PL). The Nyquist ghost remained visible in images corrected by 1D phase correction methods, but invisible in images corrected by PLACE and the proposed method. GSRs were computed from the automatically generated signal ROI and ghost ROI. One signal ROI for GSR quantification is indicated in one image by a red circle. RESULTS Phantom Results Figure 3 shows the cylindrical phantom images acquired in axial, oblique, and double-oblique imaging planes at 7T. They were reconstructed using the proposed phase labeling ghost correction method (PL), and three existing methods (Method R, Method E, and PLACE). Nyquist ghost residue remained visible by Method R and Method E in axial images, and became more obvious in oblique and double-oblique images. However, Nyquist ghost in these images reconstructed by PLACE and PL method was nearly invisible in all images. In axial images, the GSR of the proposed method was as low (1.02%) as that in PLACE (1.12%), and lower than that in Method R (3.59%) and Method E (3.24%). In oblique and doubleoblique images, the proposed method performed equally well, with GSRs of 1.05% and 1.03%, respectively, which were similar to those in PLACE (1.07% and 1.02%). In contrast, Nyquist ghost was worse and more prominent in

6 6 Xie et al. FIG. 4. EPI images of a cylindrical phantom at 7T under various eddy current conditions by changing gradient pre-emphasis settings. Eddy current was increased by adding excessive short (time constant 2 ms and gain 36%) or long (200 ms and 36%) term adjustment in readout direction on the well-adjusted Bruker MRI system. Short (2 ms and 36%) and long (200 ms and 36%) term adjustments were also made in PE or slice selection direction. Each image is displayed with normal and enhanced brightness (6). Four datasets were reconstructed with Nyquist ghost correction by Method R, Method E, PLACE, and the proposed PL method. the images corrected by Method R and Method E, with GSRs of 17.21% and 16.11% in oblique images, 20.43% and 17.36% in double-oblique images, respectively. Figure 4 shows the cylindrical phantom images acquired at 7T with gradient eddy current deliberately worsened by changing their compensations in the pre-

7 EPI Ghost and Distortion Correction 7 FIG. 5. Multislice EPI images of a phantom consisting of plastic structures within a cylindrical tube at 7T. a: Distortion free T2W images as reference. b: EPI images after Nyquist ghost correction by Method R. c: EPI images after ghost correction by Method E. d: EPI images after ghost correction by PLACE. e: EPI images after the proposed PL ghost correction (PL GC). f: EPI images in (e) overlaid with edges extracted from images in (a). g: EPI images after further distortion correction by the proposed PL method (PL GCþDC). h: EPI images in (g) overlaid with the edges extracted from images in (a). Three slices are shown, with images displayed with normal and enhanced brightness ( 8). emphasis unit to test the robustness of the proposed method for Nyquist ghost correction. Overall, the proposed method performed well in Nyquist ghost correction under various eddy current conditions, with GSR ranging from 0.99% to 1.60%. PLACE performed similarly well with GSR ranging from 1.03% to 1.72%. For Method R and Method E, GSRs were substantially higher and ranged from 3.81% to 4.00%, and 3.42% to 3.75%, respectively, which is consistent with the visual observations. Figure 5 illustrates the multislice EPI images of a cylindrical phantom with a plastic structure placed inside at 7T. Both Nyquist ghost residue and geometric distortion are visible in Figures 5b and 5c, where ghost correction was performed by Method R and Method E, respectively. With the proposed ghost correction method, ghost was well suppressed (with the average GSR in three slices as 1.04%) and became barely visible (Fig. 5e), exhibiting similar quality as PLACE (Fig. 5d). As shown in Figures 5b to 5e, phantom images exhibited severe distortion along PE direction with the cylinder image deformed into an elliptical shape and the inside horizontal structure tilted. Figures 5g and 5h show that, after further proposed distortion correction, EPI images of cylindrical phantom have been restored to a circle with the inner structures geometrically restored as well, and they were correctly aligned with the distortion free T2W reference images. Image SNR measurement results at 7T and 3T are listed in Table 1. They were measured in the images reconstructed from two frames using Method E (I10 and I20 ), the proposed method (I1 and I2 ), as well as the combined image (I 0 and I). For PLACE, SNR was measured in the combined image. Figure 6 shows the ROIs for SNR

8 8 Xie et al. FIG. 6. Cylindrical phantom images at 7T using a four-channel surface coil and 3T using an eight-channel volume head coil. ROIs for SNR assessment are indicated. calculation. Compared with Method E, SNR by the proposed method decreased approximately by 17.7% and 20.4% in the two images (I 1 and I 2 ) at 7T. For 3T images, the corresponding SNR decreases were 11.0% and 5.1%. For the combined images (I), these SNR decreases became 12.4% in 7T data and 7.1% in 3T data. PLACE yielded similar SNR performance as Method E in the combined image at both 7T and 3T data. Note that the combined images (I) yielded higher SNRs than the single-frame based images (I 0 1, I 0 2, I 1, and I 2 ). In Vivo Results Figure 7 demonstrates the in vivo multislice rat brain images acquired in the double-oblique plane at 7T. Nyquist ghost residue was still detectable after correction by Method R or Method E, but invisible after ghost correction by PLACE and the proposed method (Figures 7b to 7e, and Supporting Figure S1, which is available online). Rat brain images exhibited apparent distortion along PE direction in Figures 7b to 7e. After further distortion correction by the proposed method, they were fully corrected (Fig. 7f) and correctly aligned with the distortion free T2W images (Fig. 7h). Figure 8 demonstrates the in vivo multislice human brain images acquired in the double-oblique plane using a clinical 3T scanner. Nyquist ghost of the EPI images was corrected by Method E, PLACE and the proposed method. All methods performed well since the 3T scanner was well-adjusted. However, EPI images were affected by severe geometric distortion, especially in the frontal lobe region. After further distortion correction by the proposed method, the geometry of the images was fully restored. Careful comparison of Figures 8g to 8i reveals that the proposed method mostly eliminated the geometric distortion, whereas the parallel imaging via SENSE of two could only reduce but not eliminate the distortion. Representative fmri results at 3T are shown in Figure 9. EPI images exhibited geometric distortion after ghost correction using Method E and PLACE. With the proposed method, the brain geometry was largely restored. Activation (t-value) maps were calculated and directly overlaid on EPI and T1W reference images. In the first slice, a cluster of activated voxels was observed in the right postcentral gyrus region, which is the main sensory receptive area for the sense of touch. It can be observed in the zoomed views of slice 1 that the activated cluster calculated from fmri images without distortion correction (i.e., Method E or PLACE alone) was shifted toward the central sulcus region, and did not match well to its expected position in the postcentral gyrus. After distortion correction by the proposed method, the activated region was successfully restored to the postcentral gyrus. The time courses from three voxels exhibiting the strongest activation in each slice are also shown. They demonstrate that the time courses of the images reconstructed by the single frame based Method E were highly consistent with those by the proposed two-frame method. More importantly, their rising and falling edges of the BOLD responses overlapped to a great extent, directly indicating that the proposed method did not compromise the temporal resolution. In contrast, the rising edges of BOLD responses in PLACE were not as steep as in the other two methods, especially in block 1 of both slices, clearly indicating that the temporal resolution in PLACE was compromised. DISCUSSION Advantages of the Proposed Method This study demonstrated that the two-frame phase labeling approach in conjunction with parallel imaging could correct both Nyquist ghost and geometric distortion in EPI together. The proposed method temporally phase labels the EPI frames by modifying the PE prephase gradient to shift the central echo by one echo spacing (or odd number of echo spacings); thus, it is easy to implement on standard MRI scanners. GRAPPA weights for Nyquist ghost correction and B 0 field map for geometric distortion correction are generated from these two frames. In static imaging where only one image is required, the proposed method can effectively correct both artifacts and produce two images or one combined Table 1 Image SNRs Measured within the ROIs Shown in Figure 6, in the Images Reconstructed from Two Frames (k 1 and k 2 ) by Method E (I 0 1 and I0 2 ) and the Proposed PL Method (I 1 and I 2 ), as Well as the Combined Images (I 0 and I ) by the Three Methods a 7T 3T I 0 1 or I 1 I 0 2 or I 2 I 0 or I I 0 1 or I 1 I 0 2 or I 2 I 0 or I Method E PLACE PL Ratio(PL/E) a Respective ratios of the SNR by the proposed PL Method to that by Method E are also shown.

9 EPI Ghost and Distortion Correction 9 FIG. 7. In vivo multislice rat brain images acquired in a double-oblique plane at 7T. a: Distortion free T2W reference images. b: EPI images after ghost correction by Method R. c: EPI images after ghost correction by Method E. d: EPI images after ghost correction by PLACE. e: EPI images after ghost correction by the proposed PL method (PL GC). f: EPI images after distortion correction by the proposed PL method (PL GCþDC); (g,h) EPI images in (e,f) overlaid with brain edges extracted from images in (a). image (I1 and I2, or I in Figure 2) at the expenses of one extra frame. The proposed method is well suited for dynamic imaging such as fmri and DSC imaging, where it can correct the two artifacts using the present and next frames without incurring any extra frame or reference scan. The proposed method can robustly correct the Nyquist ghost caused by gradient time delay and eddy current. Nyquist ghost results from the inconsistency between different readout polarities, which can be caused by the gradient time delay, imperfect gradient waveform, eddy current, and local susceptibility induced gradient field. In reality, the gradient system can also be different in three physical gradient channels due to the varying eddy current or unbalanced time delay in the electronic

10 10 Xie et al. FIG. 8. In vivo multislice human brain images acquired in a double-oblique plane at 3T using an eight-channel head coil. a: Distortion free T1W images as reference. b: EPI images after ghost correction by Method E. c: EPI images after ghost correction by PLACE. d: EPI images after ghost correction by the proposed PL method (PL GC). e: EPI images after further distortion correction by the proposed PL method (PL GCþDC). f: EPI images acquired with parallel imaging using SENSE factor of 2. g i: EPI images in (d f) overlaid with the edges extracted from images in (a). components (8), which can be partially mitigated by complicated hardware compensation and adjustment procedures. Such imperfect gradient system may produce complex and high-order phase errors or inconsistency in the EPI k-space data, especially in the oblique imaging, and cause considerable Nyquist ghost. In the traditional model-based Nyquist ghost correction methods, phase inconsistency is usually modeled as either 1D or 2D linear phase error and corrected using parameters calculated from reference scan or by numerical optimization based on image entropy minimization. Thus these methods cannot correct the high-order phase

11 EPI Ghost and Distortion Correction 11 FIG. 9. Representative BOLD fmri results from a normal volunteer undergoing a left hand finger-tapping block design paradigm at 3T. EPI images were corrected by Method E, PLACE, and the proposed PL method. Activation maps were calculated and overlaid with EPI images and T1W reference images. Zoomed views of the activation regions are also shown. In the first slice, the activation region was successfully restored to postcentral gyrus region by PL method (red arrow). For each activation cluster, the time courses from three voxels with the strongest activation are plotted, with shaded areas indicating the stimulation periods. inconsistency. In our method, positive and negative echoes are separated and used to reconstruct two images using GRAPPA. This approach directly avoids the phase inconsistency among positive and negative echoes, thus making the method more robust to various phase errors. Also note that our method can preserve the single-frame temporal resolution, thus is superior to PLACE where two frames are averaged to cancel out phase inconsistency at the cost of reduced temporal resolution. For distortion correction, this method uses a field map generated from the two frames themselves, without the need to acquire it separately. In dynamic imaging, the proposed two-frame EPI can be cascaded, offering a unique advantage that the field map can be dynamically updated using two adjacent frames. Thus, B 0 field changes induced by heating and physiological fluctuation (24) can be measured and used to correct geometric distortion dynamically. This property makes our method highly attractive for dynamic imaging such as fmri, which requires long scan time and is sensitive to changes in the main magnetic field. However, there are more issues to consider. In the proposed method, both Nyquist ghost and geometric distortion correction are based on data acquired in the present and next frame, thus any motion occurring in the next frame can potentially reduce the effectiveness of the method. For rigid motion, it is possible to use rigid motion correction techniques to eliminate the phase errors or consistency in EPI k-space data (31). For local motion, Nyquist ghost and geometric distortion in the present frame may be corrected by the GRAPPA weights and field map used in reconstructing the preceding frame (14). In a more complicated scenario where continuous local motion occurs, such as in cardiac imaging, one frame is inconsistent with both the preceding and next frame, the proposed method is still expected to work because GRAPPA weights and low resolution field map are relatively insensitive to small local motion. In our fmri experiments, after applying the proposed ghost and distortion correction, any image corruption by bulk motion (e.g., as reflected by the residual Nyquist ghost) was detected by examining the barycenter of the subject in the image after correction. If the next frame shifted more than 0.2 pixel from the present frame, the present frame image was deemed to be affected by motion and was subsequently reconstructed again by the GRAPPA weights and field map used in reconstructing the

12 12 Xie et al. preceding frame, leading to robust removal of the image corruption due to the bulk motion. Further Considerations For dynamic EPI, the image SNR decreases were relatively small in the final combined image reconstructed using the proposed method compared with the entropy method (Table 1), directly indicating that the SNR efficiency was largely preserved in our method. They were 12.4% and 7.1% at 7T and 3T, respectively. During the proposed Nyquist ghost correction, GRAPPA was applied to positive and negative echoes separately to synthesize pffiffiffi the data, so the SNR was expected to decrease by 2 g in theory (32), where g is the geometric factor (g-factor). After combining the two images from positive and negative echoes, p ffiffiffi the SNR would increase approximately by a factor of 2, so the overall SNR was expected to have a loss equal to g-factor, which could vary with the actual coils and parallel imaging reconstruction algorithm. This consideration likely explained the observation that the SNR losses were generally smaller in 3T experiments (where an eight-channel volume coil was used) than in 7T experiments (where a four-channel surface coil was used). PLACE had a similar SNR performance as the entropy method, because it essentially averaged two frames. In the proposed method, any two adjacent frames are acquired with two TEs that differ by one echo spacing. This may violate the assumption that to completely eliminate the phase consistency or Nyquist ghost, two frames for the combination should have identical amplitude but opposite phase errors in the k-space. Nevertheless, the TE shift is very small, only one echo spacing. They were 0.32 ms and 0.3 ms in our 7T and 3T experiments, and negligible when compared with typical T2* value. For example, if T2* is 25 ms, one echo spacing shift of 0.3 ms only causes approximately 1% change in signal amplitude. This small amplitude change is not expected to be detrimental in the proposed ghost correction method, as generally demonstrated in our experimental results. For fmri experiments, the correction of such small but periodic signal amplitude change can be incorporated in the activation analysis, for example, by eliminating the mean difference between odd and even frames on a pixel by pixel basis, or including the confound regressor in the analysis stage to achieve better statistical outcomes. In distortion correction, the accuracy of the B 0 field map is highly dependent on the SNR of the phase maps of two images reconstructed from two adjacent frames. The phase difference map after removing phase ramp is determined by the TE shift between two frames. In the present study, the TE was shifted by one echo spacing. In theory, this shift can be equal to an odd number of echo spacings. Large shift can increase the TE difference, thus yield larger phase difference and increase phase SNR. However, it also leads to large image amplitude variation due to T2* decay, and may affect the quality of GRAPPA calibration for Nyquist ghost correction. In practice, temporal filtering may be applied to the phase difference maps during dynamic imaging to further improve the quality of field mapping and distortion correction. Although our method is described in the framework ss-epi without parallel imaging acceleration, it can be potentially combined with accelerated EPI acquisition or k-space undersampling. In essence, our method is based on sampling the full k-space lines with both positive and negative echoes to train GRAPPA weights. One possibility to combine it with parallel imaging acceleration is to use multiple frames, the number of which should be twice the acceleration factor as in TGRAPPA strategy (33,34). For example, these undersampled frames will temporally loop by twice the acceleration factor, i.e., without and with phase labeling by shifting the central echo. Together they can form a complete dataset to train GRAPPA weights, which can be used to reconstruct images from positive and negative echoes in each frame. Afterward, the field map can be computed and ghost and distortion free images are formed as similarly described in Figure 2. Another possible strategy is to combine our method with keyhole imaging technique (35), where the central k-space is fully sampled but the peripheral k- space is undersampled, and the central k-space data are used to train GRAPPA weights. However, the actual undersampling factor during parallel imaging reconstruction will be doubled when the proposed method is combined with acceleration. The g- factor related noise will increase depending on the coil setting, or can even amplify dramatically at high acceleration factor, and limit the utility of this method. As a result, the maximum possible acceleration factor that the proposed method can achieve is significantly reduced, i.e., halved. Note that these two drawbacks (noise amplification and maximum acceleration factor reduction) are also present in several other Nyquist ghost correction methods (14 17) that use the same strategy of reconstructing positive and negative echoes separately using parallel imaging. CONCLUSIONS A parallel imaging acquisition and reconstruction method has been proposed to correct both Nyquist ghost and geometric distortion together in EPI. This method uses a two-frame phase labeling strategy for parallel imaging GRAPPA calibration and subsequent image reconstruction from only positive or negative echoes for effective Nyquist ghost removal in a model free manner. Meanwhile, this phase labeling strategy shifts the TE of the second frame and allows the B 0 field map generation from positive and negative images for distortion correction. The method is relatively simple and can be potentially combined with parallel imaging acceleration. Our experimental results at 7T and 3T demonstrated that our method could greatly reduce Nyquist ghost even under oblique imaging and poor eddy current conditions, yielding significant improvements over the existing reference scan and image entropy minimization methods, and eliminate the geometric distortion. The phantom results indicated that the SNR efficiency was largely preserved while the fmri results showed no apparent degradation of temporal resolution. In summary, the proposed

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Parallel imaging acceleration of EPIK for reduced image distortions in fmri. Neuroimage 2013;73: SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article. SUP. FIG. S1. In vivo multislice rat brain images at 7T (from Figures 7b, 7c, 7d, and 7e) displayed in enhanced brightness (36) to visualize the ghost. Nyquist ghost in EPI images was corrected by Method R, Method E, PLACE, and the proposed PL method (PL GC). It remained visible in the images corrected by Method R and Method E, but not in those corrected by PLACE and the proposed PL method.