Comparison of Navigator Echo and Centroid Corrections of Image Displacement Induced by Static Magnetic Field Drift on Echo Planar Functional MRI

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1 JOURNAL OF MAGNETIC RESONANCE IMAGING 13: (2001) Technical Note Coparison of Navigator Echo and Centroid Corrections of Iage Displaceent Induced by Static Magnetic Field Drift on Echo Planar Functional MRI Ho-Ling Liu, MS, 1,2 Peter Kochunov, MS, 1 Jac L. Lancaster, PhD, 1 Peter T. Fox, MD, 1 and Jia-Hong Gao, PhD 1 * Iage displaceent caused by static agnetic field drift ay result in serious edge artifacts in echo-planar functional agnetic resonance iaging (MRI). We copared navigator echo and centroid ethods for correcting the artifacts for phanto and in vivo studies. A otor-stiulation fmri study was perfored to deonstrate the possible effects due to the displaceent. The navigator echo ethod was shown to be the superior technique for the correction of iage displaceent by effectively eliinating edge artifacts, resulting in iproved functional aps. J. Magn. Reson. Iaging 2001;13: Wiley-Liss, Inc. Index ters: MRI; functional MRI; navigator echo; otor; artifacts FUNCTIONAL MRI (fmri) using echo-planar iaging (EPI) has becoe an iportant tool in physiologic and clinical huan brain research (1). fmri easureents of subtle signal changes are very sensitive to syste instabilities. One factor that gives rise to syste instabilities during an EPI fmri study is the static agnetic field (B 0 ) drift. The shift of the central frequency ( 0 ), which is proportional to the B 0 drift, will result in iage displaceent in the phase encoding direction. If this iage displaceent is not corrected, it ay result in significant artifacts in the fmri iages. Several iage registration techniques are available for reducing otion-related fmri artifacts (2 4). For correction of a rigid body shift (eg, caused by B 0 drift), one possible ethod is by easureent of centroid displaceent (5,6) and then applying an iage shift with linear, sinc, or Fourier interpolations (7,8). The navigator echo technique has been used, besides for 1 Research Iaging Center, University of Texas Health Science Center, San Antonio, Texas Departent of Medical Technology, Chang Gung University, and Departent of Diagnostic Radiology, Chang Gung Medical Center, Taoyuan, Taiwan. Presented in part at the 7th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, 1999, Philadelphia, PA. *Address reprint requests to: J.-H. G., Research Iaging Center, University of Texas Health Science Center at San Antonio, 7703 Floyd Curl Drive, San Antonio, TX E-ail: gao@uthscsa.edu Received February 18, 2000; Accepted July 27, iage registration, to reduce otion artifacts in conventional spin-echo iaging (9), signal fluctuation in conventional gradient-echo fmri iages (10), and both through-plane and rotational otion artifacts in EPI fmri (11,12). Recently Jezzard (13) applied the navigator echo technique to eliinate the in-plane iage displaceent resulting fro the B 0 drift. To date, a coparison study of the efficiency and effectiveness of the various techniques used in correcting the iage displaceent induced by B 0 drift has not been perfored. We report our study of the evaluation and coparison of the perforance of the navigator echo and the centroid corrections for the B 0 drift induced iage displaceent in gradient-echo EPI fmri. First, we provide a brief theoretic basis for the relationship between iage displaceent and B 0 drift. Next, the results fro both the phanto and huan studies are presented to deonstrate the outcoe of the various techniques used to correct iage displaceent. THEORY In the ideal case, the relation between the NMR signal, S() at tie, and an object represented by (y), along the phase encoding direction, y, is given as S y ei2 0 Gyt ydt dy (1) where is the gyroagnetic ratio, y is the iage position in the phase-encode direction, G y (t) is the strength of the phase-encoding gradient. Eq. [1] can be written in discrete for as S e i 2/Ny (2) where N y is the total nuber of points for, and is the Fourier conjugate of. The reconstructed iage can be obtained by inverse Fourier transforation of S(): 2001 Wiley-Liss, Inc. 308

2 Corrections of Iage Displaceent in EPI fmri N y Se i2/ny (3) In the presence of a static agnetic field drift, B 0, fro the calibrated B 0, the easured NMR signal, S(), is S y ei2 0 Gyt yb0dt dy (4) Assuing B 0 is a constant within an EPI data acquisition (typically about 60-sec duration), Eq. [4] can be written in discrete for as S e i 2/Ny e i 2B0pe (5) where pe is the effective dwell tie in the phase-encoding direction. Introducing the phase difference between each phase-encode interval as pe 2B 0 pe (6) substituting Eq. [6] into Eq. [5] gives S e i 2/Ny e i pe (7) Therefore, the reconstructed iage is 1 N y 1 N y Se i 2/Ny i 2/Ny peny/2 e pen y 2 (8) where the linear phase shift in -space results in a position shift in iage space. To correct this iage displaceent, two different approaches can be used. 1. Navigator echo correction: By adding navigator echoes in the EPI sequence, pe can be easured directly, and the easured signal can be corrected to obtain the true -space data: S c S e ipe S (9) The reconstructed iage will then be identical to the original iage: c 1 N y S c e i 2/Ny (10) 2. Centroid correction: This approach involves easureent of the iage displaceent by calculating the iage-to-iage shift in the center of ass of the object, and then oving the iage bac by the aount of the displaceent. The subpixel part Figure 1. Gradient echo EPI sequence with navigator echoes ( pe 1130 sec). of the displaceent requires interpolation of the pixel values. Both linear and sinc interpolation techniques will be investigated in our studies (7,8). MATERIALS AND METHODS Experients were perfored on a 1.9-T GE/Elscint Prestige whole-body MRI scanner (GE/Elscint Ltd., Haifa, Israel) at the Research Iaging Center at the University of Texas Health Science Center at San Antonio. Infored consent was obtained fro huan volunteers after the nature of the study was explained. Three experients were conducted to assess the techniques for reoving the iage displaceent induced by the B 0 drift. Phanto Experient A cylindrical phanto with a diaeter of 8 c and a height of 22 c was filled with diethyl silicone fluid (SF96/50; Thoas Scientific, Swedesboro, NJ). This fluid iniizes the signal fluctuation due to turbulence. Transverse scans were acquired of the phanto placed on its side with its axis oriented parallel to the scanner bore. A T* 2 -weighted gradient-echo EPI sequence with navigator echoes was used. Navigator echo capability was ipleented by acquiring the first three echoes before phase encoding (Fig. 1). The zeroth-order phase difference between two phase-encode steps, pe, is calculated as half of the phase difference between the first and the third echoes to avoid a possible error due to a gradient offset between the odd and even echoes. The central frequency shift ( 0 B 0 ) can then be calculated using Eq. [6], and the iage displaceent after Fourier transforation can be obtained fro Eq. [8]. The bandwidths in the phase and readout encoding directions are and 125 Hz, respectively. Twentytwo transverse slices were iaged for each scan, with the slice thicness 6, in-plane resolution , and TR/TE/3000 s/45 s/90. For each slice, 240 iages were acquired with a total scan tie of 12 inutes. All iages were corrected for the iage displaceent (in the phase-encoding direction) by two ethods. The first ethod was the navigator echo correction accoplished by copensating for the phase difference, pe using Eq. [9]. The second ethod was to shift the iages by the difference in location of the centroid in the spatial doain using the iddle (the 120th) iage as

3 310 Liu et al. Figure 2. Exaples of raw EPI iages fro acquired the phanto (a) and in vivo (b) studies. Window and level were adjusted to deonstrate the signal-to-noise ratio and ghosting. the reference. The centroid of the ith iage, along the phase-encoding direction, y i, was calculated by y i M i x, y y x,y M i x, y x,y (11) where M i is the agnitude of the ith iage, is a rectangular set of pixels containing the phanto iage. Both linear and Fourier interpolations (8) were used to ipleent the centroid correction. For evaluation, the root ean square error of the displaceent correction (E rs ) noralized to the ean iage intensity were copared for both techniques. The E rs of the ith iage was calculated by E rs,i 1 N M i x, y M 120 x, y 2 (12) x,y where N is the nuber of pixels in. In Vivo Experient A huan subject s brain was iaged in this study. The subject s head was restrained in a olded plastic facial as to reduce otion. The iaging data acquisition and data analysis were identical to the phanto experient as described earlier. fmri Experient For the functional study, four right-handed subjects were ased to perfor three tass: rest (control), rightfist flexion, and left-fist flexion. In the fist-flexion tass, the subjects repeatedly opened and closed the corresponding hand. For the EPI acquisition, 20 iages per slice were acquired for each state, and two cycles were perfored, with a total of 120 iages per slice and a 6-inute acquisition tie. The subject s head was restrained in a olded plastic facial as to iniize otion artifacts. Acquisition paraeters and correction schees perfored were identical to those in the phanto and in vivo experients described earlier, with the exception of a different total nuber of iages (and acquisition tie), and the fact that the reference iage used for the centroid corrections was the 60th iage. For precise anatoic detail, a T1-weighted iage was acquired, using a conventional spin-echo sequence, with the sae slice location as that used for functional iaging. Maps of activation were calculated by coparing iages acquired during the tas state with those during the control state. A t test was perfored with a threshold of 2.5 (P 0.01). Regions with fewer than four contiguous activated pixels were excluded fro the functional ap (14). The activation ap then was overlaid on the corresponding T 1 iage. To evaluate the reduction in edge artifact fro different correction techniques, the percentage reduction of the activated voxels along the edges of the brain, fro the activation ap before correction, was deterined in each subject. RESULTS Exaples of raw EPI iages fro both phanto and in vivo studies are shown in Fig. 2 to deonstrate the iage quality. Figure 3 shows the iage displaceent along the phase-encoding direction (easured by centroid displaceent) and corresponding 0 shift (easured by navigator echoes) for a phanto (a) and a huan subject (b). The relationship between iage displaceent and 0 ( B 0 ) was obtained fro Eq. [6] and Eq. [8]. During the scan tie of 12 inutes, an iage displaceent as large as two pixels (corresponding to 5.8 ) was observed for our MRI scanner. Figure 4 shows the E rs for the corrections with the navigator echo and centroid techniques for both the phanto (a) and the huan subject (b). Larger errors resulted fro the use of the centroid ethod for both the phanto and the huan subject. For the centroid ethod, linear interpolation caused larger errors than Fourier interpolation in the phanto experient. No significant difference between the two interpolation algoriths was observed in the huan experient. The otor-stiulation fmri iages shows a siilar pattern for four subjects, and one of the subjects is illustrated in Fig. 5. There are a strong edge artifact without applying any correction and soe residual edge artifacts after centroid corrections (as shown in the Fig. 4a f). The ean and standard deviation of the percentage reductions of this edge artifact across subjects were 89% 8%, 93% 7% and 100% 0, for the centroid correction with linear interpolation, the cen-

4 Corrections of Iage Displaceent in EPI fmri 311 iage space, whereas navigator echoes provide a direct easureent of the corresponding phase change in space. A coparison of the navigator echo technique with other otion-correction techniques, applied to the B 0 drift proble, would certainly be of practical interest and should be studied in the future. For the displaceent easureent using the centroid ethod, the residual N/2 EPI ghosts can be a significant source of error in the correction process. In the first experient, a sall phanto was used to avoid overlap of ghosts and the iage. In addition, the ghosts were separated and excluded fro the centroid calculation. The navigator echo and centroid easureents of iage displaceent were found to be in close agreeent (as shown in Fig. 3a). Thus the larger E rs of the centroid ethods (Fig. 4a) is believed to be ainly due to the interpolation algorith. However, the larger error fro the centroid ethod with Fourier interpolation, copared with the navigator echo ethod, ight be due to the sall inaccuracy in the shift detection. For the huan subject, the ghosts overlapped with the brain and could not be separated fro the iages. Therefore they were included in the calculation of the centroid. Consequently, the iage displaceents easured by the navigator echo and centroid ethods, as shown in Fig. 3b, differed ore than they did in the phanto study. In this case, the inaccuracy of the centroid easureent was the ain reason for the larger errors. Figure 3. Iage displaceent and central frequency shift ( 0 ) easured by centroid and navigator echoes for stability studies on a phanto (a) and a huan subject (b). troid correction Fourier interpolation, and the navigator echo technique, respectively. DISCUSSION We have deonstrated that the iage displaceent due to B 0 drift can result in significant artifacts in the EPI fmri iages. The cause of this tie-dependent B 0 drift is currently under investigation. Tests perfored on our syste show a correlation of this B 0 drift with the duty cycle of the sequence (data not shown). Consequently, it is suspected that the B 0 drift ay be caused by high-duty cycle EPI eddy current induced heating of the surrounding aterials (including shiing etals). In theory, this syste instability can be perfectly corrected by using the phase inforation provided by the navigator echoes. However, practically, the B 0 drift coupled with real patient otion or physiological fluctuation can be a coplicated issue. Cobining the navigator echo technique with a otion-correction algorith (2 4,7 12) ay provide a better solution, although this issue requires further investigation. The centroid ethods perfored in this study are siplified versions of other retrospective otion-correction techniques [eg, Autoated Iage Registration (2,3)], which use the sae translation algorith but different displaceent-detection ethods. They were used for coparison because the centroid is a direct easureent of the B 0 drift induced displaceent in Figure 4. E rs for centroid and navigator echo corrections for the stability studies of the phanto (a) and a huan subject (b). The range of y coordinates was adjusted to provide better visualization of the E rs.

5 312 Liu et al. In the fmri experient, we deonstrated an exaple of the artifacts caused by the iage displaceent and the residual effects observed when different correction techniques were applied. In general, the artifacts result fro the change of the contrast-to-noise ratio between blocs in the fmri signal tie course, which are the cobined effects of B 0 drift pattern, tas design, subject otion, and the individual variety of the responses. After the statistical threshold process, they can appear as edge artifacts, soothing of the functional ap, and/or dislocation or eliination of the detected activation sites. In this experient, artifacts at the posterior edge are due to the directional iage displaceent, which results in an increasing trend in the pixel intensity tie course. For the data set shown in Fig. 5, the activation at the right otor area during the left fist flexion tass could be seen only after using the navigator echo correction (Fig. 5g). In suary, iage displaceent induced by a B 0 drift can cause isleading results in EPI fmri. In this study, navigator echo and centroid corrections were evaluated and copared. Both ethods reduced the fmri artifacts by correcting the bloc iage shift in the phase-encoding direction. The navigator echo ethod was shown to be the superior technique, resulting in iproved functional aps. ACKNOWLEDGMENTS We than Dr. Peter Jezzard, Lisa Nicerson, and Trevor Andrews for helpful discussion. Figure 5. Functional activation due to left-fist flexion (a, c, e, g) and right-fist flexion (b, d, f, h) before correction (a, b), after centroid correction with linear interpolation (c, d), after centroid correction with Fourier interpolation (e, f), and after navigator echo correction (g, h). [Color figure can be viewed in the online issue, which is available at co.] REFERENCES 1. Kwong KK. Functional agnetic resonance iaging with echo planar iaging. Magn Reson Q 1995;11: Woods RP, Grafton ST, Holes CJ, Cherry SR, Mazziotta JC. Autoated iage registration: I. General ethods and intersubject, intraodality validation. J Coput Assist Toogr 1998;22: Woods RP, Grafton ST, Watson JDG, Sicotte NL, Mazziotta JC. Autoated iage registration: II. Intersubject validation of linear and non-linear odels. J Coput Assist Toogr 1998;22: Friston KJ, Ashburner J, Frith CD, Poline JB, Heather JD, Fracowia RSJ. Spatial registration and noralization of iages. Hu Brain Mapp 1995;2: Oppenhei BE. A ethod using a digital coputer for reducing respiratory artifact on liver scans ade with a caera. J Nucl Med 1971;12: McKeighen RE. Iproved eans of correcting otion blurring in scintigraphic iages. Phys Med Biol 1979;24: Hajnal JV, Saeed N, Soar EJ, Oatridge A, Young IR, Bydder GM. A registration and interpolation procedure for subvoxel atching of serially acquired MR iages. J Coput Assist Toogr 1995;19: Eddy VF, Fitzgerald M, Noll DC. Iproved iage registration by using Fourier interpolation. Magn Reson Med 1996;36: Ehan RL, Fellee JP. Adaptive technique for high-definition MR iaging of oving structures. Radiology 1989;173: Hu X, Ki S-G. Reduction of signal fluctuation in functional MRI using navigator echoes. Magn Reson Med 1994;31: Lee CC, Jac CR, Gri RC, Rossan PJ, Fellee JP, Ehan RL, Riederer SJ. Real-tie adaptive otion correction in functional MRI. Magn Reson Med 1996;36: Lee CC, Gri RC, Manduca A, Fellee JP, Ehan RL, Riederer SJ, Jac CR. A prospective approach to correct for inter-iage head rotation in fmri. Magn Reson Med 1998;39: Jezzard P. Effects of B 0 agnetic field drift on echo planar functional agnetic resonance iaging. In: Proceedings of the ISMRM 4th Annual Meeting, New Yor, p Xiong J, Gao J-H, Lancaster JL, Fox PT. Clustered pixels analysis for functional MRI activation studies in huan brain. Hu Brain Mapp 1995;3: