1 Introduction

Combining spectral and spatial information, Magnetic Resonance Spectroscopic Imaging (MRSI) provides distribution maps of metabolites. In standard experiments, the spatial information is obtained through phase encoding, requiring the acquisition of a number of scans at least equal to the number of voxels in the spectroscopic image. The spectral information is obtained through spin-echo or FID acquisition. In ¹H MRS, due to the high number of metabolites that can be detected in the brain, the narrow spectral range (around 10 ppm) of their resonances, the multiplet structure of J-coupled resonances, and the line broadening caused by the inhomogeneities of the local B₀ field, the peaks overlap, making quantification for mapping difficult.

Use of two-dimensional J-resolved spectroscopy is one way to avoid the peak overlap that 1D MRS suffers from. In 2D J-resolved spectra, the spectral information is spread onto a map: the chemical shift is encoded in the t₂ direction and the J coupling in the t₁ direction. It has been shown that 2D spectroscopic information can be combined with spatial encoding [1]. However, to obtain 2D spectroscopic images with high 2D spatial resolution, the acquisition time becomes excessive. For example, with a repetition time of 1 s, 32 encoding steps in both spatial directions, and 40 time increments, the minimum acquisition duration is longer than 11 h (without accumulation): this long duration strongly limits the biomedical use of such 4D techniques.

The minimum acquisition time of 4D SI can be reduced by using fast SI techniques based on various fast imaging solutions, including U-FLARE [2], echo-planar [3], multi-coil array [4] and spiral imaging [5]. Among these methods developed to reduce the minimum number of scans, the echo-planar SI based methods, for instance the Spiral Spectroscopic Imaging (SSI), use the delay between two successive time-domain points to sample spatial information. In SSI, the minimum acquisition time is reduced by applying a series of readout gradients during the acquisition window to collect simultaneously spatial and chemical shift information. Thanks to fast spiral encoding of the 2D spatial domain, the acquisition of t₁ data can be achieved in a reasonable time. On the other hand, a good quality of the gradient hardware, a gridding algorithm and the measurement of the actual k-space trajectory become necessary to obtain a spectroscopic image.

We propose a k-space trajectory waveform based on continuous series of growing and shrinking (‘out-and-in’) spirals [6] instead of just growing spirals, as are usually used in SSI [7]. Adding to the advantages of spiral imaging, like symmetry of k-space apodization by transverse relaxation effects, symmetry of gradient hardware demands, etc., out-and-in spiral k-space trajectories increase the robustness of SSI against the artefacts of flow and motion thanks to its readout gradient moment nulling, and also avoid specific rewinding gradients to return to the centre of k-space.

We present a high-spatial-resolution 4D out-and-in SSI experiment performed on rat brain at 7 T, and the data processing necessary to reconstruct the spiral spectroscopic images. The quality of the image is evaluated by spatial-resolution estimation, and signal-to-noise measurement.

2 Method

2.1 Spiral spectroscopic imaging pulse sequence

During the rising (falling) part of each out-and-in spiral module, N_rot rotations are accomplished at constant angular velocity β = 4 π N_rot/T. The spiral radius increases or decreases linearly with time between 0 and k_max, at rate α = k_max/T [8]. A single rotation takes T/(2 N_rot) second, and the radius changes by k_max/N_rot at each turn. Using complex notation, the k-space trajectory curve (k(t) = k_x(t) + i k_y(t)) is described for a single out-and-in spiral module of duration T by:  

$$\mathrm{k}\left(\mathrm{t}\right)=\mathrm{i}\alpha \mathrm{t}\exp \left[–\mathrm{i}(\beta \mathrm{t}+2\pi \mathrm{s}/{\mathrm{N}}_k)\right]\mathrm{for}0\le \mathrm{t}<\mathrm{T}/2$$

and  

$$\mathrm{k}\left(\mathrm{t}\right)=\mathrm{i}\alpha (\mathrm{T}-\mathrm{t})\exp \left[\mathrm{i}(\beta (\mathrm{T}-\mathrm{t})-2\pi \mathrm{s}/{\mathrm{N}}_k)\right]\mathrm{forT}/2\le \mathrm{t}<\mathrm{T}$$

(1)

A circular k-space region of diameter 2 k_max is covered (Fig. 1). Segmentation in k-space is achieved by the initial phase term 2 π s/N_k, where s = 0, ... N_k–1 is varied between acquisitions of the N_k k-space interleaves [9]. N_dat points were acquired during each spiral module.

In the t₂ domain, to sample the information over a spectral bandwidth SW (inverse of the sampling time DW), a single spiral should start every DW. At high field, to cover the 10-ppm bandwidth (¹H MRS spectral width), DW is shorter than at low field. Depending on the hardware limitations for gradient rise-time, it may be not possible to sample all the data associated with a particular k-space plane within such a short DW, so temporal interleaves may be required. N_spiral out-and-in spiral modules were applied after each excitation, and N_t2 temporal interleaves were acquired by delaying by DW the opening of the acquisition window and, therefore, the start of the spiral readout gradients (Fig. 2). A total of N = N_t2 N_k N_spiral N_dat points were thus sampled during N_t2 N_k excitations that encoded the k_x, k_y, and t₂ domains. To describe the t₁ domain, N_t1 increments were achieved by echo-time incrementation, leading to a total experiment time of N_t2 N_k N_t1 TR N_a where TR is the repetition time and N_a the number of averages. More details can be found in [6].

Before the out-and-in spiral readout gradients, the volume of interest (VOI) was selected with a PRESS (Point-Resolved Spectroscopy) sequence [10] (Fig. 3). The PRESS sequence was preceded by a CHESS (Chemical Shift Selective) module for water suppression [11] and an outer-volume-saturation (OVS) module to decrease spatial contaminations.

3 Results

Digital resolutions of 6.1 Hz and 2.0 Hz per point were achieved in the f₂ and f₁ domains respectively. The resonances of N-acetylaspartate (NAA) at 2.0 ppm, glutamate/glutamine (Glu) at 2.4 ppm, creatine (Cre) at 3.0 ppm and choline (Cho) at 3.2 ppm were clearly observed on a 2D spectrum extracted from SSI datasets (Fig. 4). Fig. 5 shows the Cr (3.0 ppm) image computed from spiral spectroscopic datasets.

To evaluate the actual spatial resolution of the spectroscopic image, the theoretical point-spread function (PSF) was computed as a function of k-space sampling, gridding and spatial filtering (Fig. 6). The voxel size of the spectroscopic experiment was estimated to be 27.0 μl by numerical integration of the volume of the PSF function scaled to slice thickness.

The SNR was calculated from the intensity of the phased NAA peak divided by the noise r.m.s. measured between 6 and 8 ppm. For 10 pixels spaced by more than the PSF FWHM (3 mm) of the SSI dataset, the average SNR was 16.3 ± 4.6.

4 Discussion

An in-vivo 2D J-resolved spiral spectroscopic image with 16 steps in t₁ and a 20 × 20 spatial matrix was achieved with a SNR higher than 16, in 42 min 40 s against 4 h 26 min for a standard phase encoding MRSI. The dependence of the PSF function on T₂^*, or on the chemical shift was not taken into account in the theoretical calculation, so the actual voxel size can be slightly larger than the 27 μl estimated from the SSI PSF.

The in-vivo high-resolution out-and-in SSI method combines high strength spiral readout gradients (up to 87.3 mT m^–1) and rapid commutations (up to 0.83 T m^–1 ms^–1). This probably leads to a significant deviation between the theoretical and the actual k-space trajectories due to eddy currents, gradient system limits and pre-emphasis settings. To avoid all artefacts caused by this deviation, the actual k-space trajectory measured according to [14] was used to reconstruct the spectroscopic image.

Three-dimensional gridding was avoided by considering that the time-domain was regularly sampled throughout the data acquisition. First-order phase correction was used for data interpolation within a spectral dwell-time: gridding can be a time-consuming process, and our approach may be an advantageous alternative.

The k-space oversampling, resulting in a FOV of 48 mm, prevents the replica sidelobes produced by the gridding algorithm from being folded into the image of interest, and reduces the aliasing artefacts from the acquisition truncature. After the inverse FFT in the spatial domain, the data points outside of the FOV of interest were discarded, and only the data corresponding to a FOV of 30 mm containing the rat brain were kept and processed further.

Compared with standard spiral encoding, out-and-in spiral encoding somewhat increases the time efficiency of the sequence since all the data points collected in the acquisition window are used for image reconstruction. Moreover, thanks to the time symmetry of the gradient waveform, leading to periodically null gradient moments, the sensitivity to motion is further reduced, as recently demonstrated by Kim et al. [15].

5 Conclusion

We have demonstrated the feasibility of fast spiral 2D-spectral 2D-spatial spectroscopic imaging at high field in vivo. Mono-voxel clinical 2D spectroscopy has recently been proved useful for obtaining more information for spectral characterization and to better assign the resonances [16–18]. Robust rapid spectroscopic imaging techniques open the way to clinical applications of 2D spectroscopy.

Acknowledgements

The authors thanks R. Farion for the animal preparation, J.A. Coles and L. Lamalle for helpful discussions. B.H. received a grant from the ‘Association pour la recherche contre le cancer’. The NMR facilities were supported in part by the ‘Programme Interdisciplinaire Imagerie du petit animal’ (CNRS–INSERM, France)