Chemical exchange saturation transfer (CEST) imaging has been introduced as a new contrast mechanism for molecular imaging, and typically requires long saturation preparation and multiple acquisitions of imaging data with varying saturation frequencies (called z-spectrum)^1,2. Since the z-spectrum acquisition is inherently slow and takes prohibitively long imaging time, it has been very difficult to introduce CEST z-spectrum into a clinical routine. In this work, we propose a novel, simultaneous multi-slice (SMS) Spiral CEST encoding with Hankel subspace learning (HSL)^3,4 for ultrafast whole-brain z-spectrum acquisition within 2-3 minutes, in which: 1) RF segmented uneven saturation is employed to reduce the duration of saturation preparation⁵, 2) Spiral CEST encoding is employed to acquire SMS signals, and 3) SMS signals are projected onto the subspace spanned by the complementary null space, selectively reconstructing a slice of interest while nulling the other slices.

1) SMS-HSL Reconstruction: The proposed SMS scheme models the SMS Hankel-structured matrix as the linear superposition of Hankel matrices of all excited slices $$$\bf{N_s}$$$ :

$$\bf{\mathcal{H}\left ( y\right ) = \sum_{m=1}^{N_s} \mathcal{H}\left ( x_m \right ) + N}$$

where $$$\bf{\mathcal{H}\left (\cdot\right )}$$$ is the Hankel operator, $$$\bf{y}$$$ is the measured SMS signals in k-space, $$$\bf{x_m}$$$ is the desired k-space at the m^th slice, and $$$\bf{N}$$$ is the additive noises. To selectively estimate the slice of interest while nulling the other slices, Hankel composite matrix is constructed by combining all slices other than a slice of interest $$$\bf{\mathcal{H}\left ( x_s^c \right ) = \sum_{m=1}^{N_s} \mathcal{H}\left ( x_m \right ) - \mathcal{H}\left ( x_s \right )}$$$, and the complementary null space $$$\bf{\mathcal{N}_s^c}$$$ is then learned taking right singular vectors corresponding to small singular values below a certain value following SVD (Fig. 1). By projecting $$$\bf{\mathcal{H}\left ( y \right )}$$$ onto the subspace spanned by $$$\bf{\mathcal{N}_s^c}$$$, the slice of interest $$$\bf{\mathcal{H}\left ( x_s \right )}$$$ can be well-separated from $$$\bf{\mathcal{H}\left ( y \right )}$$$ suppressing most of the contribution of $$$\bf{\mathcal{H}\left ( x_s^c \right )}$$$ while holding the signal components of $$$\bf{\mathcal{H}\left ( x_s \right )}$$$ intact:

$$\bf{\mathcal{H}\left ( y \right )\mathcal{N}_s^c=\mathcal{H}\left ( x_s \right )\mathcal{N}_s^c}$$

Exploiting the facts that $$$\bf{\mathcal{H}\left ( x_s^c \right )}$$$ has a non-empty null space and $$$\bf{\mathcal{H}\left ( x_s \right )}$$$ is highly rank-deficient (Fig. 1), the reconstruction is posed as an optimization problem by simultaneously imposing null projection and low-rank prior with data consistency:

$$\bf{\hat{x}_s = \underset{x_s}{min} \ \ \frac{1}{2}\left \| \mathcal{H}\left ( y\right ) - \sum_{m=1}^{N_s} \mathcal{H}\left ( x_m \right ) \right \|_F^2 + \frac{\lambda_N}{2}\left \| \left ( \mathcal{H}\left ( y \right ) - \mathcal{H}\left ( x_s \right ) \right ) \mathcal{N}_s^c \right \|_ F^2 + \lambda_L \left \| \mathcal{H}\left ( x_s \right ) \right \|_*}$$

where $$$\bf{\lambda_N}$$$ and $$$\bf{\lambda_L}$$$ are regularization parameters. The complementary null spaces are estimated from CEST reference scan, and the optimization is solved using variable splitting method by alternating between well-defined sub-problems.

2) Experimental Evaluation: To test the feasibility of the SMS-HSL in accelerating CEST imaging, we performed the SMS acquisition on a 2D whole-brain spiral CEST datasets with RF-segmented uneven irradiation. The CEST sequence consists of two saturation pulses, each of which lasted 3sec and 0.5sec, respectively. All images were acquired with a spatial matrix 64x64 using a single-shot spiral trajectory through 32receiver coils, and 21different offset were performed varying from -5 to 5ppm with a frequency interval of 0.5ppm. The total scan time for acquiring whole-brain with 30slices was 7min 50sec, and the reference scan was performed without saturation pulse for CEST normalization and SMS calibration. The proposed SMS-HSL reconstruction was compared with Split slice-GRAPPA (SP-SG) as a competing method.

Fig. 2 shows the five sets of brain images with CEST labeling frequency of 3.5ppm, and the image was reconstructed using SP-SG and SMS-HSL, respectively, when an MB factor is set to 5. The SP-SG suffers from severe amplified noises over the entire images while the SMS-HSL relatively reduces artifacts leading to robust reconstruction of brain structures. Fig. 3 compares the corresponding z-spectrum reconstructed using fully sampled standard CEST data, SP-SG, and SMS-HSL for white and gray matter regions, respectively. It is observed that SP-SG results in larger deviation of the reconstructed z-spectrum from the standard MT signals while SMS-HSL remains close to the standard MT signals in both white and grey matter regions.We successfully demonstrated that the proposed, spiral CEST encoding with SMS-HSL can produce ultrafast whole-brain z-spectra within 2-3minutes (clinically feasible imaging time) without apparent loss of SNR. It is expected that the proposed method may introduce CEST z-spectrum acquisition into a clinical routine in the future.