JOURNAL OF MAGNETIC RESONANCE 132, 150–153 (1998) ARTICLE NO. MN981396 COMMUNICATIONS Simple Correction Method for k-Space Trajectory Deviations in MRI Jeff H. Duyn, 1 Yihong Yang, Joseph A. Frank, and Jan Willem van der Veen Laboratory of Diagnostic Radiology Research and CBDB, National Institutes of Health, Building 10, Room B1N-256, Bethesda, Maryland 20892 Received September 23, 1997 A method is presented to correct for the imperfections of spatial In the following we introduce an alternative method to encoding gradients in MRI. The approach is simple and fast, can measure actual k-space trajectories in MRI. This method be performed with standard scanner hardware, and does not require does not involve the use of a reference phantom, is easy to separate measurements with reference phantoms. The new method, implement, and requires only two pulse sequence repetitions using the MR signal to accurately measure the k-space trajectory of per spatial encoding axis. the imaging sequence, allows for correction of gradient hardware imperfections and eddy-current effects. Initial measurements are METHODS presented which demonstrate the efficacy of the method to correct images acquired with spiral and EPI scan techniques. The new method measures the actual k-space trajectories Key Words: fast MRI; gradient hardware; k -space; correction of small subsets of spins, at various locations in the magnet, methods. similar to the approach proposed by Mason et al. ( 4 ). In the current method, instead of using a small reference phan- tom, the subsets of spins are selected by conventional slice INTRODUCTION selection, at positions displaced from the isocenter of the gradient system ( Fig. 1 ) . This requires only a minor modifi- Fast MR scan sequences such as EPI ( 1 ) and spiral imaging cation of the actual pulse sequence. For each direction of ( 2 ) put high demands on gradient hardware, thereby requiring spatial encoding ( e.g., phase encode and readout directions ) , highly effective suppression of eddy current effects. Inadequa- a measurement is performed with the slice select gradient cies in gradient hardware or incomplete elimination of eddy switched to the corresponding gradient axis, while encoding current effects leads to deviations in the targeted k-space trajec- gradients in all other axes are switched off. A second scan tory, and generally results in image artifacts. is performed with all spatial encoding gradients switched One way to compensate for these gradient imperfections off (Fig. 1), in order to allow for elimination of effects of is to measure the actual k-space trajectories and use this switching the slice select gradient direction on the k-space information during image reconstruction. Several methods trajectory. From the difference Df between the accrued have been suggested to estimate this trajectory. For situations phases of the two measured MR signals, with negligible eddy currents, Spielman and Pauly ( 3 ) have used a method which measures the current through the gradi- ent coils. Mason et al. ( 4 ) have proposed a method which Df r ( t ) Å  t 0 gr G r ( t )r D r rdt Å D r rk r ( t ), estimates the actual k-space trajectory from the MR signal. It performs several calibration measurements involving a with small reference phantom placed at off-isocenter locations in the magnet bore. Finally, the method described by Onodera g Å gyromagnetic ratio et al. ( 5 ) and modified by Papadakis et al. ( 6 ) uses a so- called self-encoding gradient pulse preceding the acquisition G r ( t ) Å spatial encoding gradient amplitude interval and performs an long series of MR acquisitions with r Å encoding direction ( x , y , or z ) various gradient amplitudes. D r Å distance of the slice to gradient isocenter, 1 To whom correspondence should be addressed. Fax: (301) 402-3216. E-mail: jhd@helix.nih.gov. the k-space trajectory k r ( t ) can be simply derived by nor- 150 1090-7807/98 $25.00