One of the primary goals of magnetic resonance spectroscopic imaging (MRSI) is to spatially resolve a spectrum in each voxel within a 2D slice or 3D volume. Conventional MRSI uses phase encoding for each spatial dimension, which can result in long scan times.

Echo-planar sampling of k-t space significantly reduces imaging time. Similar to echo planar imaging (EPI) in MRI, an entire k-space slice is sampled in each TR, significantly reducing the total acquisition time.

Echo-planar MRSI however, experiences measurement errors far greater than phase encoded MRSI due to longer readout times, increased sensitivity to B₀ field inhomogeneity, and larger readout gradient amplitudes. The scanner’s gradient system often fails to produce the programmed gradient waveforms perfectly because of hardware imperfections and physical effects, including limited coil and amplifier bandwidth, eddy currents, mutual coupling of gradient channels, mechanical vibrations, thermal variations.

These deviations from the expected gradient field significantly impact the results of echo-planar-based MRSI techniques.

Non-Cartesian echo planar spectroscopic imaging—using concentric circular, spiral, radial, and rosette trajectories—is particularly sensitive to k-t sampling deviations due to the constantly changing gradient directions during the readout period or across multiple spatial interleaves. Thus, correcting k-space misregistration in echo-planar-based MRSI is essential to minimize imaging and spectral artifacts in the final metabolic maps.

One way to correct misregistration in k-t space is to fully characterize the temporal behavior of gradients and recompute the sampling coordinates before reconstruction. The gradient system can often be modeled as linear and time-invariant, allowing prediction of the gradients’ temporal behavior using the gradient impulse response function (GIRF) for each axis. GIRF estimated trajectories have been shown to improve reconstruction of MR images (Vannesjo et al. 2016).

The GIRF can be measured with a dynamic field camera (Vannesjo et al. 2013).

Here we present an example of how GIRF-based corrections can enhance the spatial-spectral quality of FID-MRSI with rosette trajectories at 7T.

Relevant MRSI parameters for the discussion in this article are listed below:

• Field of view = 256 mm × 256 mm, matrix size = 128 × 128
• Nominal in-plane resolution =2.0 mm × 2.0 mm with slice thickness = 10 mm.
• Spectral resolution: 2500 Hz / 512 = 4.9 Hz (after two spectral interleaves)
• Fully sampled k_x-k_y space with 200 petals
• Readout duration: 207.2 ms per interleaf
• Total scan time: 15 minutes

In using a GIRF to correct rosette spectroscopic imaging, we expect:

1. Improvements in artifacts in metabolite maps,
2. Lipid contamination to be minimized, and
3. Improved spectral quantitation.

These improvements are directly due to the accurate estimation of the rosette k-space trajectory. The nominal k-space trajectory does not include scanner-based field fluctuations. These fluctuations are part of the image encoding.

Full details of the MRSI acquisition and reconstruction can be found here:
Saucedo et al., “Effect of gradient impulse response function-based corrections on high resolution FID rosette spectroscopic imaging at 7T”, upcoming in Proceedings of ISMRM 2025, Abstract 2752.

GIRF prediction of trajectory shows deviation from nominal k-space trajectories

Figure 1: (A) Left – nominal and GIRF-predicted G_x gradient (shown for 3 “spectral” time points); Right – Zoom-in showing that the scanner does not reach the expected maximum gradient amplitude (23 mT/m) (B) Left – GIRF-corrected and nominal k-space trajectory comprised of a subset of 10 petals. Right – Zoom-in showing deviations of the GIRF-corrected k-space coordinates compared to the nominal coordinates.

Reconstructions based on GIRF-corrected k-space lead to greater SNR and reduced artifacts

The figure below shows that the trajectory of the first 800 µs of the readout is different than the last 800 µs of the readout in reality. The nominal trajectory shows they should be the same. Thus, understanding the precise temporal behavior of the gradients is crucial not only for correcting k-space misregistration but also for accounting for phase evolutions that influence temporal sampling of the spectral dimension.

Figure 2: (A) Top row: nominal (black) and GIRF-predicted (red) k_x-k_y coordinates from the 1st TR. (B) Zoomed-in view of the central k-space area, showing the distortion of the rosette trajectory caused by deviations in the actual gradients, at the 1st (red) and 256^th (blue) time points. (C) Water maps from GIRF-corrected and uncorrected reconstructions in brain, indicating signal loss in the cranium and a lower SNR in the uncorrected maps. (D) Water maps in phantom, demonstrating recovery of SNR and image features (red arrows) in GIRF-corrected reconstructions.

Reduction of imaging artifacts in metabolite maps from in vivo brain and phantom data

In vivo metabolite maps from GIRF-corrected reconstruction show a significant reduction in artifacts and fewer areas where metabolite quantitation exceeded a Cramer-Rao lower bound (CRLB) of 30%.

Figure 3: (A) Localization for an in vivo 2D FID Rosette MRSI acquisition. The 10mm slice was placed axially immediately above the corpus callosum. (B) Top row: Metabolite maps from GIRF-corrected (top row) and uncorrected (bottom row) reconstructions of total n-acetylaspartate (tNAA: NAA+NAAG), total creatine (tCr: Cr+PCr), total choline (tCho: GPC+PCh), myo-inositol (mI), and glutamate (Glu). (C) Maps of the Cramer-Rao lower bounds (CRLB) from LC Model quantitation of GIRF-corrected and uncorrected reconstructions, shown up to a maximum of 30%.

GIRF-corrected reconstructions of phantom data produced metabolite maps with reduced inhomogeneity and lower estimates of the CRLBs throughout the phantom, indicating improved quantitation reliability.

Figure 4: (A) Localization for a 2D FID Rosette MRSI acquisition in a spectroscopy phantom. (B) Top row: Metabolite maps from GIRF-corrected (top row) and uncorrected (bottom row) reconstructions of n-acetyl-aspartate (NAA), creatine (Cr), choline (Cho), myo-inositol (mI), glutamate (Glu), and lactate (Lac). (C) Maps of the Cramer-Rao lower bounds (CRLB) from LCModel quantitation of GIRF-corrected and uncorrected reconstructions, shown up to a maximum of 30%.

Reduction of lipid contamination in surrounding voxels and improved spectral quality

GIRF-corrected spectroscopic images from the slice-based FID acquisition, which also excites cranial lipid signals, show a significant reduction in lipid contamination in brain voxels. This decrease in lipid “bleeding” into adjacent voxels enhances spectral quantitation. The improvement occurs because the underlying PSF is more accurately represented in the GIRF-corrected k-space. In phantom data, the most notable enhancement is the gain in SNR.

Figure 5: (A) Region-of-interest (ROI-yellow box) in which spectra from each voxel are shown overlaid in (C). (B) Lipid maps showing increased lipid “bleeding” due to Gibbs ringing in the uncorrected map. The GIRF-corrected map is more in focus, limiting the extent of lipid contamination in the voxels within the brain region. (C) Overlaid spectra in the ROI, showing a greater degree of lipid contamination and baseline distortion in uncorrected data. (D) Overlaid phantom spectra within the yellow ROI, showing a gain of SNR in the GIRF-corrected data.

Improved spectral quantitation

Figure 6 illustrates enhanced quantitation, indicated by lower CRLBs and reduced variation in the metabolite-to-tCr ratios. The metabolite-to-tCr ratios for GIRF-corrected phantom data align more closely with expected values.

To assess repeatability across six in vivo scans, the coefficients of variation (CVs) were:

• tNAA/tCr: 27% (GIRF-corrected), 68% (uncorrected)
• tCho/tCr: 24% (GIRF-corrected), 75% (uncorrected)
• mI/tCr: 44% (GIRF-corrected), 70% (uncorrected)
• Glu/tCr: 34% (GIRF-corrected), 147% (uncorrected)

Figure 6: (A) Mean CRLBs in phantom, before and after GIRF-based corrections. (B) Means and standard deviations (error bars) of metabolite ratios in phantom. (C) Means and standard deviation of CRLBs for selected metabolites over 6 in vivo scan sessions. (D) Means and standard deviations of metabolite ratios over the entire brain region across six in vivo scans, indicating greater coefficients of variance (CV%) of the ratios from uncorrected vs GIRF-corrected data particularly for Glu/Cr – 1.3±0.4 (34%) vs 1.4±2.1 (147%). (E) Histograms of mI/tCr and Glu/tCr in gray and white matter.

In conclusion, GIRF corrections significantly enhance reconstruction fidelity and quantitation accuracy for high-resolution rosette FID-MRSI, in both phantom and in vivo studies. By incorporating GIRF-predicted k-space coordinates in echo-planar-based MRSI, we compensate for cumulative gradient-induced phase errors that impact spatial and spectral encoding during the readout period. Addressing gradient imperfections is essential for non-Cartesian MRSI, especially in high-resolution acquisitions that require optimal gradient performance.