provide good correction for concomitant gradients in non-isocenter scans. Introduction: In MRI, a linear field gradient is typically applied to encode spins.
Rapid Correction for Concomitant Gradient Field Effects in Spiral Scans C. T. Sica1, C. H. Meyer1 1
University of Virginia, Charlottesville, VA, United States
Abstract: A rapid image reconstruction method employing a linear fit to correct for concomitant gradients was developed to reduce blurring in spiral scans. An analysis was performed to determine the effect of concomitant gradients in oblique spiral scans, including the effects of physical offsets and fitting selective parts of the field map. The method was tested on spiral scans with physical offsets and compared with a frequency-segmented reconstruction. The worst-case orientation is halfway between sagittal and coronal. Image results show the linear fit alone is a quick method to provide good correction for concomitant gradients in non-isocenter scans. Introduction: In MRI, a linear field gradient is typically applied to encode spins. In reality, the resulting field contains not only a linear gradient but also higher-order terms, which can be modeled via a Taylor expansion. These higher-order terms, termed concomitant gradients, create off-resonance frequencies as quadratic functions of space1. These can warp the k-space trajectory and modulate the k-space data, leading to unwanted blurring effects, especially in spiral scans. King et al. showed that a frequency-segmented reconstruction can remove this blurring, although at the cost of significant computation2. We propose a rapid method employing a linear fit to the concomitant gradient field map, which can be used to correct the kspace data at little computational cost. Methods: For a given oblique orientation and physical offset in a spiral scan, a field map consisting of off-resonance frequencies can be calculated2. A linear fit to the field map can be calculated quickly3, either over the whole field map or selective parts of the map, which produces a set of fitting parameters. These fitting parameters are then used to correct the k-space trajectory and the raw k-space data3. To determine the worst orientation, multiple field orientations were calculated, and the worst case of each field map was recorded (see Fig.1). Cases were also tested with physical offsets in different directions, as well as fitting to selective parts of the field map, to better understand the behavior of the field maps. Data corresponding to worst case orientations were obtained with a spiral sequence using a tag pattern, the tags making it easier to see the blurring. Deblurring was applied via two methods, a Figure 1: The left diagram represents a summation over many frequency-segmented reconstruction method using the concomitant gradient field map, and a linear fit to the concomitant gradient field map that was used to correct the raw orientations, each points represents the highest off resonance frequency for a given orientation. The max is 327 Hz. The right is data and k-space trajectory before reconstruction. The frequency correction varies the field map for the data below, the max is 313 Hz at the edges. during the readout as a squared function of the spiral gradient magnitude. Results: The worst-case scan-plane orientation at isocenter is halfway between sagittal and coronal. The worst case results in maximum in-plane frequency variation from concomitant gradients. The best-case orientation is axial, which has only a through-plane effect2. The linear fit results in no change for a slice through isocenter with a centered FOV, but reduces blurring for any other prescription. The effect of the linear fit for an offcenter slice is to reduce the blurring to a level similar to a centered isocenter slice. Performing a selective fit to a subsection produces superior fitting results within the selection, but at the expense of weaker fitting outside the selection. Figure 2 contains the deblurring results for an orientation halfway between sagittal and coronal, with the center of the FOV offset along physical z by 3.5 cm. The linear fit was a selective fit centered on the phantom. As can be seen, the uncorrected phantom clearly demonstrates blurring, especially on the edges (see inset). The best correction is via the frequency segmented method, and the linear fit is very close in quality. The field map for this case had a maximum of 313 Hz on the edges (Fig 1b) Conclusion: Blurring from concomitant gradient fields is a significant issue for spiral scans with 40 mT/m gradients at 1.5T, especially for nonisocenter prescriptions and longer readouts. The method described represents a quick way to correct for these effects. The overall effect of this correction is to make the blurring pattern similar to the blurring pattern for an isocenter scan. Spiral scans should be designed to be tolerant of this blurring level or frequency-segmented deblurring should be used. A selective fit to part of the field map will produce the best fit, which leads to the possibility of deblurring some parts of the image well at the expense of other parts. A potential application for this method is real-time cardiac MRI, where the heart is usually offset from isocenter and reconstruction speed is important. Additionally, using the linear fit prior to the frequency reconstructed method could speed up the latter. By decreasing the range of off-resonance frequencies with the linear fit beforehand, the number of bins in the frequency segmented method drop, reducing computation time. Figure 2: The three images, from left to right: 1) No correction; 2) Linear fit; 3) Frequency segmented. Note the minimal difference in blurring between the second and third inset. Image data: Siemens 1.5T Sonata, 40 mT/m maximum spiral gradient amplitude, 20 interleaves, readout time: 16.4 ms, resolution: 0.63 mm by 0.63 mm, FOV: 24 by 24 cm (17 cm by 17 cm displayed). Orientation: Halfway between sagittal and coronal. Center of FOV is offset 35 mm from isocenter along physical z and center of phantom is offset 50 mm.
References 1. Bernstein at al. Magn Reson Med, 39: 300-308 (1998) 2. King K et al. Magn Reson Med 41, 103-112 (1999) 3. Irarrazabal P et al. Magn Reson Med 35, 278-282 (1996)
Proc. Intl. Soc. Mag. Reson. Med. 11 (2003)
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