Correction for EPI Distortions Using Multi-Echo Gradient-Echo Imaging

Correction for EPI Distortions Using Multi-Echo Gradient-Echo Imaging Nan-kuei Chen and Alice M. Wyrwicz* Magnetic Resonance in Medicine 41:1206 1213 (1999) A novel and effective technique is described for distortion correction in echo planar imaging (EPI) utilizing the field maps derived from multi-echo gradient-echo images. The distortions from different off-resonance related factors such as field inhomogeneity, eddy current effect, radiofrequency pulse frequency offset, and chemical shift effect can be simultaneously reduced to a great extent. With the proposed post-processing algorithm of multi-channel modulation, distortions may be corrected without unwrapping the phase discontinuities in the derived field map, a process that usually restricts the application of other field map-based correction methods. Results from phantom and animal experiments at 4.7 T demonstrate the efficiency of the method in reducing the geometrical distortions in gradient-echo EPI. Magn Reson Med 41:1206 1213, 1999 1999 Wiley-Liss, Inc. Key words: echo planar imaging (EPI); geometrical distortions; multi-channel modulation; field mapping Echo planar imaging (EPI), first proposed in 1977 (1), is becoming increasingly popular as a rapid imaging method in many applications, including functional MRI (fmri), dynamic imaging with a contrast agent, diffusion-weighted imaging, and cardiac imaging. The main drawback of EPI is its sensitivity to the off-resonance related factors, such as B o field inhomogeneity, chemical shift effect, radiofrequency (RF) frequency offset, and the eddy current effect from the fast switching gradients. Weisskoff and Davis (2), and Jezzard and Balaban (3) demonstrated that the image distortion arising from B o field inhomogeneity can be greatly reduced using a field map calculated from offset spin-echo images or double-echo gradient-echo images. Both methods require that phase discontinuities in the field inhomogeneity map be unwrapped (4,5) before the derived field map can be applied to correct the geometrical distortions in image domain (3) or to modulate the k-space data in Fourier domain (2). Since the field map derived from gradient-echo or spin-echo images encodes only B o field inhomogeneity, EPI distortions resulting from other off-resonance related factors, such as eddy current effect, cannot be corrected. A correction algorithm that uses multiple EPI-based field maps (6) would provide field inhomogeneity information in the distorted coordinates and reduce geometrical distortion more efficiently. Wan et al. (7) suggested that image distortion from both B o field inhomogeneity and eddy current effects can be reduced by using multi-reference scans instead of field mapping. In their approach, the distortion was corrected by directly multiplying EPI k-space data with a filter computed from Center for MR Research, ENH Research Institute, and Departments of Biomedical Engineering, Neurobiology and Physiology, Northwestern University, Evanston, Illinois. Grant sponsor: National Institutes of Health; Grant number: GM53175. *Correspondence to: Alice M. Wyrwicz, Center for MR Research, 1033 University Place #150, Evanston, IL 60201. Received 27 July 1998; revised 18 January 1999; accepted 23 January 1999. 1999 Wiley-Liss, Inc. 1206 the reference scans. Their derivation is based on the assumption that spatial distribution of field inhomogeneity is a slowly varying function. This assumption is invalid in the presence of chemical shift and strong susceptibility effects near the tissue/air or tissue/bone interfaces, especially at a high magnetic field. Based on the limitations of the prior methods, we propose a new technique that simultaneously corrects the EPI distortions from different off-resonance related factors including the chemical shift effect, RF frequency offset, field inhomogeneity, and the eddy current effect from fast switching readout gradients. These off-resonance related factors generating EPI distortions can be encoded with a multi-echo gradient-echo sequence and corrected with the proposed post-processing algorithm, multi-channel modulation. The complicated phase unwrapping procedure (4,5), which restricts the applications of other field map-based correction methods (2,3,6), is completely avoided in the proposed technique. The acquisition time of multi-echo gradient-echo images for encoding field inhomogeneity information is longer than that of EPI, and it would appear that the single-shot capability of EPI is compromised in the proposed distortion correction method. However, in applications with repeated measurements, such as fmri and dynamic contrast agent studies, the extra scan time spent on field mapping is not excessive. The present method makes it possible to register correctly low-resolution EPI data (64 64 or 128 128) with high-resolution conventional images that exhibit good anatomical details. Accurate registration of EPI and anatomical image is especially important in fmri studies. It is assumed that there is no movement of the scanned object between the EPI scan and field mapping in the method described. THEORY The acquisition trajectories of gradient-echo EPI and multiecho gradient-echo imaging in 3D reciprocal space, which represents the phase accumulation as a function of k space and time (8), will be described and compared first. Then the principles of EPI distortion correction with the multichannel modulation method will be discussed. It will be shown that the phase maps generated from the multi-echo gradient-echo images can be used to correct EPI distortions without the phase unwrapping procedure. Implementation of distortion correction for one-way and two-way k-space sampling EPI will also be demonstrated. Gradient-Echo EPI and Multi-Echo Gradient-Echo Imaging Trajectories in 3D Reciprocal Space In EPI acquisition, all the k-space data points are acquired after a single excitation of the spin system. The sampling

Distortion Correction for EPI 1207 FIG. 1. (a) The gradient-echo EPI pulse sequence with one-way k-space sampling and its scanning trajectory in 3D reciprocal space. (b) The pulse sequence of multi-echo gradient-echo imaging and its scanning trajectory. The 3D reciprocal space data of the multi-echo gradient-echo image encodes majority of the off-resonance related factors in EPI acquisition, since the same readout gradient waveforms are used in the two pulse sequences. trajectory can be zigzag, sinusoidal, or rectangular (9), depending on the gradient waveforms. In this paper, the blipped gradient-echo EPI sequence is used for data sampling in a rectangular trajectory, which can be directly Fourier transformed to reconstruct the image without interpolation or regridding (10). Figure 1a presents the gradient-echo EPI pulse sequence with one-way k-space sampling, in which only the data points in odd echoes are sampled. Ignoring the relaxation effects, the acquired k-space data, S 1 (m k x, n k y, l T), with the matrix size N x N y can be represented as S 1 (m k x, n k y, l T) (x, y) exp (im k x x) exp (in k y y) (x, y, l T) dx dy, N x /2 m N x /2, N y /2 n N y /2, l n N y /2 where (x, y) is the spin density of the scanned object, k x [1] and k y are the incremental steps in k-space for spatial encoding along readout and phase-encoding directions, respectively, and T is the inter-echo time interval (time duration between two consecutive odd echoes). (x, y, l T) is the phase error term along the phase-encoding direction, originating from the off-resonance related factors. It can be represented as (x, y, l T) exp (i2 l (x, y) l T) [2] where l (x, y) is the spatial function of all off-resonance related factors including main field inhomogeneity, eddy current effect from switching readout gradients, eddy current effect from phase-encoding gradient blips, and chemical shift effect. We note that l (x, y) may vary between different k y lines since eddy current effects are time dependent. The phase error term along the readout direction is not considered in Eqs. [1] and [2]. Since the bandwidth per pixel along the readout direction is usually larger than the inhomogeneity term l (x, y) in actual EPI experiments, EPI distortions along the readout direction are less than a pixel and are neglected. The EPI trajectory of one-way k-space sampling, as presented in Eq. [1], covers an oblique plane in the 3D reciprocal space (plane ABGH in Fig. 1a).

1208 Chen and Wyrwicz The raw data acquired with the multi-echo gradient-echo sequence (Fig. 1b) can be represented by Eqs. [3] and [4]: S 2 (mk x, n k y, l T) (x, y) exp (im k x x) exp (im k y y) (x, y, l T) dx dy, N x /2 m N x /2, N y /2 n N y /2, 0 l N y (x, y, l T) exp (i2 l (x, y) l T) [4] It can be seen that Eqs. [1], [2] and Eqs. [3], [4] differ in two aspects: 1) the raw data presented in Eqs. [3] and [4] cover a volume of 3D reciprocal space (Fig. 1b), and the data presented in Eqs. [1] and [2] cover an oblique plane (Fig. 1a); and 2) the eddy current effect due to phase blips is encoded in the l (x, y) term of Eq. [2] but not in the l (x, y) term of Eq. [4], since they are not used in the multi-echo gradient-echo pulse sequence. The magnitudes of phase gradient blips are usually quite small in actual EPI experiments; therefore the image distortions resulting from phase gradient eddy current effect are much smaller than those originating from other off-resonance related factors. The 3D reciprocal space data from multi-echo gradientecho acquisition encode most off-resonance related factors in EPI such as main field inhomogeneity, chemical shift effect, frequency offset of RF pulse, and eddy current effect from readout gradients, as indicated by Eqs. [1], [2] and [3], [4]. Therefore, most geometrical distortions in EPI can be corrected using the phase maps derived from the multiecho gradient-echo images. Implementations of EPI distortion corrections using the information from the multi-echo gradient-echo images will be shown later. Conventional Method of Phase Modulation vs. Multi-Channel Modulation Weisskoff and Davis (2) suggested that the geometrical distortions in EPI can be corrected with the method of phase modulation. In their approach, the corrected image is obtained by modulating the distorted image in the Fourier domain. The modulated k-space data S o (m,n) are first calculated from the distorted EPI image EPI(p, q) and a modulating factor F(n), as shown in Eq. [5], [3] k-space data S o (m, n). In this approach, the spatial distribution of field inhomogeneity (p, q) must be obtained before modulated k-space data can be calculated with Eq. [5]. The field map derived from offset spin-echo images or a double-echo gradient-echo image cannot reveal the actual value of field inhomogeneity because of the phase wrapping artifact. Therefore, the phase discontinuities in the derived field map must be unwrapped (4,5). The phase unwrapping procedure is usually complex and not robust, especially in the presence of a strong susceptibility or chemical shift effect. Therefore, the application of the field map-based phase modulation method is restricted. Analysis of Eq. [5] indicates that the phase unwrapping procedure can be avoided if the modulating factor F(n) in Eq. [5] for each k y line is experimentally generated from two gradient-echo images with the echo time difference equal to the phase accumulation time n T in the corresponding k y line. Based on this premise, a new algorithm termed multi-channel modulation that calculates each k y line of the modulated k-space data through different channels is proposed. The distortion-free EPI image can be generated with multi-channel modulation algorithm without the complication of the phase unwrapping procedure. With the multi-channel modulation, the image may be transformed from distorted to non-distorted coordinates, and vice versa. In the algorithm shown in Fig. 2a, the distorted EPI image is calculated from two inputs, a distortion-free gradient-echo image (input 1), and multiple phase maps (input 2). Each of the multiple phase maps is simply the unit length ratio, as defined in Eq. [6], of two gradient-echo complex images. The arctangent function is not performed in our algorithm Input 2 ( th map) R exp (i )/R [6] where R exp(i ) is a complex ratio of the th echo-image to the 1st echo-image, and R is the absolute value of the ratio. For example, if 64-echo gradient-echo images are acquired using the pulse sequence in Fig. 1b, then 64 unit-length-ratio phase maps in non-distorted coordinates (input 2 in Fig. 2a) can be directly calculated from those echo images utilizing Eq. [6]. As shown in Fig. 2a, the modulated k-space data in different k y lines are calculated through different channels. For example in the th channel, the th modulated k y line (S(m, n )) is obtained from the distortion free gradientecho image (Input 1 (p, q)) and the th phase map (Input 2 (p, q, )) with Eq. [7]. S 0 (mn) p q EPI(p, q) exp (i2 mp/n x ) exp (i2 nq/n y )F(n) F(n) exp ( i2 0 (p, q) n T) N x /2 p N x /2, N y /2 q N y /2, N x /2 m N x /2, N y /2 n N y /2, where 0 (p, q) is the field inhomogeneity map and T is the inter-echo time interval. The corrected EPI image is then obtained by taking the Fourier transform of the modulated [5] S(m, n ) p Input 1 (p, q) q exp (i2 mp/n x ) exp (i2 q/n y ) Input 2 (p, q, ), N x /2 p N x /2, N y /2 q N y. /2, N x /2 m N x /2 [7]

Distortion Correction for EPI 1209 FIG. 2. The schematic diagram of the multi-channel modulation (a) The distorted EPI k-space data and image (output 1 and 2) are calculated from a distortion free image (input 1) and multiple phase maps (input 2) using multi-channel modulation. (b) EPI k-space data and image in the non-distorted coordinates (output 1 and 2) are generated from a distorted EPI image (input 1) and multiple phase maps in the distorted coordinates (input 2). The gradient-echo image in distorted coordinates (output 2) can then be obtained by taking the Fourier transform of the modulated k-space data S(m, n) (output 1). It will be shown later that images transformed to distorted coordinates (output 2 of Fig. 2a) provide necessary information for the EPI distortion correction (Fig. 2b). The reversed process of Fig. 2a is shown in Fig. 2b, which converts EPI images (input 1) from distorted to non-distorted coordinates (output 2) using the phase maps in distorted coordinates (input 2). From the theoretical point of view, the two algorithms shown in Fig. 2a and 2b are parallel. However, input 2 in Fig. 2b, unlike input 2 in Fig. 2a, cannot be directly calculated from the experimental data. Instead, the phase maps in distorted coordinates are generated from the distorted echo images that form the output 2 of Fig. 2a. The unit-length-ratio phase maps in distorted coordinates are calculated from these distorted images using Eq. [6] and become the input 2 of Fig. 2b. The distorted EPI images can now be transformed to nondistorted coordinates as shown. Distortion Correction for Gradient-Echo EPI With One-Way k-space Sampling The geometrical distortions in one-way acquisition EPI can be corrected using the algorithm presented in Fig. 2. The multi-echo gradient-echo images, acquired with the pulse sequence shown in Fig. 1b, are transformed from non-distorted to distorted coordinates using Fig. 2a. The multiple phase maps in distorted coordinates are then derived from the transformed images in distorted coordinates using Eq. [6], and are used as input 2 in Fig. 2b. Distortion-free EPI images can thus be calculated using the multi-channel modulation algorithm shown in Fig. 2b. Distortion Correction for Gradient-Echo EPI With Two-Way k-space Sampling Acquiring k-space data in both polarities of readout gradients results in an additional ghost artifact due to the misalignment between odd and even echoes. The ghost artifact can be reduced through use of the non-linear correction method (10), in which each k y line is shifted based on the non-phase-encoded reference scan. The nonlinear correction method is applied to both EPI and multiecho gradient-echo image data to eliminate the misalignment of odd and even echoes before performing the multi-channel modulation. With this non-linear correction method, most N/2 ghost artifact and some of the geometrical distortions in EPI are removed. The remaining geometrical distortions are then corrected using the multi-channel modulation method.

1210 Chen and Wyrwicz MATERIALS AND METHODS Experiments were performed on a GE Omega 4.7 T system fitted with actively shielded gradient coils, capable of generating the maximum amplitude of 18 Gauss/cm. Parameters for gradient-echo EPI with one-way k-space sampling were inter-echo time interval 1408 sec, gradient rise time 96 sec, bandwidth 125 khz, and total acquisition time 98 msec for a 64 64 image matrix. The acquisition gate was kept on after the excitation RF pulse, and the digitized data were acquired during both flat and ramping periods of the readout gradients. To sample a rectangular trajectory, sufficient data points (64 complex pairs) were acquired during the flat period, and the oversampled data from the ramping period were discarded. Therefore, there was no need to use the re-gridding algorithm in image reconstruction (10). A phantom consisting of water-filled tubes was used to examine the efficiency of the proposed method in correcting the distortions originating from B o field inhomogeneity, susceptibility effect, and the eddy current effect. A transverse slice of the phantom was imaged with slice thickness 2mm, matrix size 64 64, and field of view (FOV) 48 48 mm. After a single-shot gradient-echo EPI acquisition, a 64-echo gradient-echo image was acquired using the pulse sequence shown in Fig. 1b with a TR of 1 sec. Sixty-four phase maps were generated from the 64-echo gradient-echo image data by calculating the ratio of each image to the first-echo image, and conversion to the distorted coordinates using the algorithm shown in Fig. 2a. A distortionfree EPI image was then generated with the multi-channel modulation (Fig. 2b), after the phase maps in distorted coordinates were calculated from the converted echo images. The second phantom, consisting of a water-filled tube and an acetone-filled tube, was used to evaluate the effectiveness of the method described in correcting the chemical shift distortion. The experimental parameters were the same as in the first phantom experiment except the FOV was 60 60 mm. The chemical shift difference between water and acetone corresponded to 400 Hz in our experiment. Since each pixel corresponds to 11.1 Hz along the phase-encoding direction, a linear shift of 36 pixels between water and acetone images was expected in the phase-encoding direction. The correction technique for two-way k-space sampling EPI was tested on rabbit brain in vivo. The EPI image of a 2 mm thick coronal slice was acquired with inter-echo time interval 704 sec, FOV 60 60 mm, and total scan time of 53 msec for a matrix size of 64 64. After the EPI scan, a 64-echo gradient-echo imaging data was acquired using the same readout gradient waveforms. To eliminate the N/2 ghost artifacts, a non-phase-encoded reference scan with the phase gradient disabled was also acquired. The nonlinear correction method was then applied to both EPI and multi-echo gradient-echo data to remove the artifacts originating from the misalignment between odd and even echoes. Sixty-four phase maps in distorted coordinates were generated from the multi-echo gradient-echo image data, using the same approach as in one-way k-space sampling EPI. The distortion-free EPI image was then obtained from the algorithm shown in Fig. 2b using the distorted EPI image and phase maps in distorted coordinates. The correction algorithms were implemented in IDL software (Research Systems, Boulder, CO) installed on a Sun Ultra workstation (Sun Microsystems, Mountain View, CA). RESULTS AND DISCUSSION The distortion correction algorithm was first tested on a water phantom, which consisted of a 25 mm tube containing a number of smaller tubes. Two types of geometrical distortions can be identified in the one-way k-space sampling gradient-echo EPI image (Fig. 3a). A global shift of the image by 6 pixels, which originates from the RF pulse frequency offset, is observed along the phase-encoding (vertical) direction. Geometrical deformation due to B o field inhomogeneity and eddy current effect is also seen. The corrected EPI image presented in Fig. 3b demonstrates that both global shift and geometrical deformation can be removed by the multi-channel modulation method. The 32 nd echo image of the multi-echo gradient-echo data, which has the same effective echo time and spatial resolution as the EPI image, is presented in Fig. 3c as the reference image for comparison. Since there is no need to calculate the actual field inhomogeneity map using the unwrapping technique, the FIG. 3. Images of the phantom consisting of a water-filled cylinder with a number of smaller tubes inside (a) Geometrical distortions are visible in the one-way k-space sampling gradient-echo EPI image. (b) Distortions are corrected using the multi-channel modulation. (c) The reference image is the 32 nd echo image of the multi-echo gradient-echo image data.

Distortion Correction for EPI 1211 FIG. 4. Images for the phantom comprised of water (upper image) and acetone (lower image), two components with different chemical shifts (a) Water and acetone gradient-echo EPI images are distorted due to B 0 field inhomogeneity, and shifted along the phase encoding (vertical) direction because of the chemical shift difference. (b) Image distortions arising from different off-resonance related factors are simultaneously corrected with the multi-channel modulation. (c) The reference image is the 32 nd echo image of the multi-echo gradient-echo image data. (d) The spatial distribution of field inhomogeneity is illustrated in the arctangent function of the 32 nd unit-length-ratio phase map. multi-channel modulation method can be easily applied to a case in which both chemical shift effect and B o field inhomogeneity are present. This is illustrated in Fig. 4 for a phantom comprised of water and acetone, two components with different chemical shifts. Three different types of geometrical distortions are visible in the uncorrected EPI image (Fig. 4a). A 36 pixel separation between the water and acetone images along the phase-encoding (vertical) direction arises from the chemical shift difference. A global shift along the phase-encoding direction due to the RF frequency offset is observed. The geometrical deformations of both water and acetone images as a result of B o field inhomogeneity and eddy current effect can also be identified. All three types of geometrical distortions are effectively removed in the EPI image after correction with the multi-channel modulation algorithm (Fig. 4b). The 32 nd echo image is presented in Fig. 4c as a reference, and the corresponding 32 nd unit-length-ratio phase map is shown in Fig. 4d to illustrate the spatial distribution of field inhomogeneity. Abrupt phase changes originating from water/acetone chemical shift difference and 2 boundaries due to rapid field variation are observed. Distortion correction of this image would be difficult with methods that require phase unwrapping procedures (2,3) or assume a slowly varying field (7). Although no theoretical assumption is used in deriving the algorithm of multi-channel modulation, there is in fact a limitation when the algorithm is applied to the chemical shift distortion correction. Only partial correction can be achieved when images from different chemical shift components overlap spatially within the same pixel in the distorted coordinates. This problem can be avoided by application of either Dixon s method or spectral/spatial RF excitation, so that components of the chemical shift system are separated or pre-saturated before the EPI distortion correction. Since the purpose of the experiment in Fig. 4 was to demonstrate the capability of the algorithm to remove distortions simultaneously from different sources, we chose the simplest chemical shift system in which EPI images of different chemical shift components do not spatially overlap. The multi-channel modulation was tested on a rabbit brain image acquired with the two-way k-space sampling gradient-echo EPI sequence. As shown in Fig. 5a, both the N/2 ghost artifact and the geometrical distortions are seen. The N/2 ghost artifact in two-way EPI, which is a result of the misalignment between even and odd echoes, is removed first using the non-linear correction method with non-phase-encoded reference scan. Although the N/2 artifact and part of the distortions can be removed by the non-linear correction method, residual geometrical distortions, such as the image elongation indicated by arrows in Fig. 5b, are still visible. The residual distortions are corrected through the use of the multi-channel modulation FIG. 5. Coronal slice images of the rabbit brain (a) The N/2 ghost artifact arising from odd-even-echo misalignment is severe in the two-way k-space sampling gradient-echo EPI image. (b) The N/2 ghost artifact is reduced with the non-linear correction method. The residual geometrical distortions (arrows) are still visible. (c) The residual distortions are corrected with the multi-channel modulation. (d) The reference image is the 32 nd echo image of the multi-echo gradient-echo image data.

1212 Chen and Wyrwicz method. Comparison of the corrected EPI image (Fig. 5c) and the reference distortion-free image (Fig. 5d) illustrates that the proposed algorithm removes most geometrical distortions in two-way k-space sampling gradient-echo EPI image. Techniques for N/2 ghost reduction utilizing phaseencoded reference scan (11) and comparing odd and even echoes of EPI itself (12) were recently reported. These methods have a better tolerance to B o field inhomogeneity and may replace the non-linear correction method in our current implementation. In either case, both raw EPI and multi-echo gradient-echo data must be corrected using the same reference scan. The effectiveness of other distortion correction methods that are based on field mapping (2,3) would be severely reduced if the phase unwrapping procedure fails due to phase map noise. On the other hand, the performance of our multi-channel modulation algorithm is much less dependent on the phase map noise because the phase unwrapping procedure is not performed. Although the noise in the phase maps acquired at longer echo time might reduce the accuracy of the modulated high k y lines in our method, the affected high k y data have little effect on the corrected EPI image quality. The multi-channel modulation algorithm is capable of removing different distortions simultaneously by using the field inhomogeneity information encoded in multi-echo gradient-echo images. Although this inhomogeneity information was available in the multi-reference approach of Wan et al. (7), those authors corrected EPI distortions in a different way without using all the available information in multi-reference scans. In our method, distortions are removed by using a modulation process involving both k-space and image domains. It can simultaneously correct severe distortions originating from different off-resonance related factors, as shown in this paper. In the method of Wan et al. (7), EPI distortions are reduced by using a k-space domain filter, which is computed from only a small portion of the acquired multi-reference scans. Since their derivation is based on the assumption that the spatial distribution of field inhomogeneity is a slowly varying function, the performance of such an approach might be degraded when this assumption is invalid in the presence of chemical shift and strong susceptibility effects. The pulse sequence shown in Fig. 1b is in effect an echo planar spectroscopic imaging (EPSI) sequence reported earlier by Posse et al. (13,14). Both spatial and spectral information can be obtained from the 3D reciprocal space data (Fig. 1b) when 3D Fourier transform is performed. However, different data matrix sizes are used in EPSI application and in the multi-channel modulation method. In EPSI, low spatial and high spectral resolution is usually selected (e.g., 32 32 512), so that a detailed metabolic spectrum can be mapped spatially. The multi-channel modulation method requires identical data size along the phase-encoding spatial axis and time axis (64 64 64 in our implementation), so that each k y line can be modulated using the corresponding phase map with the same phase accumulation time. The described distortion correction method can be applied to EPI with different readout gradient waveforms as long as the readout gradients used in both EPI and multiecho gradient-echo imaging are identical. This technique can also be used to correct distortions in EPI with different phase-encoding ordering schemes (e.g., segmented EPI), when the correspondence relation between modulated ky lines and phase maps (Fig. 2) follows the same ordering of phase encoding. The present implementation of multichannel modulation is not as effective for two-shot insideout EPI (15) artifact removal. Additional phase correction and data manipulation would be needed to remove image blurring and ghosting artifact originating from the phase discontinuities near the zero ky line of inside-out EPI. CONCLUSIONS The EPI geometrical distortions arising from different off-resonance related factors, including chemical shift and readout gradient eddy current effects, can be corrected simultaneously with the method of multi-channel modulation. Since the complex phase unwrapping procedure is avoided, the proposed method can be easily applied to in vivo animal and human EPI data even in the presence of strong susceptibility effects near the tissue/air and tissue/ bone interfaces. Results from phantom and animal gradientecho EPI with one and two way k-space sampling demonstrate the efficiency and effectiveness of this new distortion correction method. The present technique can be applied to fmri studies, to generate distortion-free activation maps and provide accurate co-registration between EPI-based fmri data and high-resolution anatomic image. ACKNOWLEDGMENTS The authors thank Drs. P.N. Venkatasubramanian, L. Li, and K. Bahk for valuable discussion, and Dr. Y.-J. Shen for assistance in animal preparation. This work was supported by the National Institutes of Health grant GM53175 to A.M.W. REFERENCES 1. Mansfield P. Multi-planar image formation using NMR spin-echoes. J Phys C 1977;10:L5 L58. 2. Weisskoff RM, Davis TL. Correcting gross distortion on echo planar images. In: Proceedings of the SMRM 11th Annual Meeting, Berlin, 1992. p 4515. 3. Jezzard P, Balaban RS. Correction for geometrical distortion in echo planar images from Bo field variations. Magn Reson Med 1995;34:65 73. 4. Liang Z-P. A model based method for phase unwrapping. IEEE Trans Med Imaging 1996;15:893 897. 5. Zhang W, Goldhaber DM, Kramer DM. 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