Ilya Chugunov^{1}, Wissam AlGhuraibawi^{2}, Kevin Godines^{2}, Bonnie Lam^{2}, Frank Ong^{3}, Jonathan Tamir^{1,4}, and Moriel Vandsburger^{2}

^{1}Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, United States, ^{2}Bioengineering, University of California, Berkeley, Berkeley, CA, United States, ^{3}Electrical Engineering, Stanford University, Stanford, CA, United States, ^{4}Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, United States

Multiscale low rank reconstruction has been demonstrated to efficiently reconstruct non-gated dynamic MRI by leveraging sparsity in the time domain. This abstract demonstrates its ability to reconstruct 4-fold accelerated CEST imaging of the heart via similarly exploiting sparsity in the Z-spectrum domain. This reconstruction outperforms zero-filled IFFT for quantization of magnetization transfer, nuclear overhauser, and CEST effects as derived from Lorentzian-line-fit analysis. Extension to volumetric or motion inclusive CEST imaging and development of a new regularization function may enable further acceleration.

The acquired image sequence is proposed to be represented by:

$$\mathbf{x}_{z}=\sum_{j=1}^{J} \mathcal{M}_{j}\left(\mathbf{L}_{j} \mathbf{R}_{j}[z]^{H}\right)$$Where $$$\mathbf{x_z}$$$ is a CEST acquisition image at offset index $$$z$$$, represented by a summation over $$$j \in [1, ..., J]$$$ block scales. Here, $$$\mathbf{L_{j}}$$$ are block spatial bases, $$$\mathbf{R_{j}}[z]$$$ are Z-spectrum bases, and $$$\mathcal{M}_{j}$$$ embeds an input block matrix into the acquired image.

The resultant parallel k-space acquisitions $$$y_{zc}$$$ at offset $$$z$$$ and channel $$$c$$$ are modeled by:$$\mathbf{y}_{zc}=\mathbf{F}_{z} \mathbf{S}_{c} \sum_{j=1}^{J} \mathcal{M}_{j}\left(\mathbf{L}_{j} \mathbf{R}_{j}[z]^{H}\right)+\mathbf{w}_{zc}$$Where $$$\mathbf{F}_z$$$ is the Fourier sampling operator, $$$\mathbf{S}_c$$$ is the sensitivity map operator, and $$$\mathbf{w}_{zc}$$$ is white Gaussian noise.

The objective is then to find optimal bases $$$\mathbf{L_{j}}$$$ and $$$\mathbf{R_{j}}[z]$$$ which minimize:$$f(\mathbf{L}, \mathbf{R})=\sum_{z=1}^{Z} \frac{1}{2}\left\|\mathbf{y}_{z c}-\mathbf{F}_{z} \mathbf{S}_{c} \sum_{j=1}^{J} \mathcal{M}_{j}\left(\mathbf{L}_{j} \mathbf{R}_{j}[z]^{H}\right)\right\|_{2}^{2}+\sum_{j=1}^{J} \frac{\lambda_{j}}{2}\left(\left\|\mathbf{L}_{j}\right\|_{F}^{2}+\left\|\mathbf{DR}_{j}\right\|_{F}^{2}\right)$$Where the left side of the equation is the total reconstruction error for acquisitions $$$z \in [1, …, Z] $$$, and the right is a regularization factor, weighted by $$$\lambda_j$$$, which requires the manual selection of one global regularization parameter $$$\lambda$$$. Here, an optional transform operator $$$\mathbf{D}$$$ can be applied to the Z-spectrum bases. We use finite differences to promote smoothness both spatially and along the Z-spectrum domain.

The method was tested on cardiac CEST scans acquired on a 3T Siemens Trio scanner (Siemens Medical Systems, Erlangen, Germany) from 10 healthy volunteers with IRB approval and informed consent, with no history of cardiovascular disease, diabetes, or smoking, aged 20-37. A scan consisted of 52-56 segmented echo planar gradient echo acquisitions, each corresponding to a point on the produced Z-spectrum. Parameters as follows: FOV = 300 x 253mm, spatial resolution = 1.56 x 1.56mm, slice thickness = 8mm, TR = 4.7ms, TE = 2.59ms, and FA = 25°, timed to end-diastole.

Sensitivity maps $$$\mathbf{S}_c$$$ were calculated via JSENSE reconstruction

Overall, MSLR reconstruction on retrospectively under-sampled data significantly outperforms zero-filled IFFT in the measure of creatine CEST signal amplitude (figure 5), and shows comparable reconstruction of NOE and amide CEST. Both reconstruction methods show a very high deviation in MT center from fully sampled scans, however the associated Lorentzian has full width at half max (FWHM) magnitudes larger than the other four pools, and the effect of a large shift in its center frequency is minor.

While CEST and NOE amplitudes in the IFFT reconstructions were equally often underestimated and overestimated in scans at varying accelerations, MSLR reconstruction always led to higher calculated amplitudes than the fully-sampled scans.

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Figure 1. Example fully sampled cardiac CEST MRI scan. a) Graph of the produced Z-spectrum points for septal region of the heart, overall Lorentzian-line-fit, and breakdown of the 5 contributing factors for which individual Lorentzian functions were fit. b) Sample CEST acquisitions at varying offsets (green tick marks indicate center of CEST region and corresponding points on Z-spectrum).

Figure 2. Example reconstruction results for 2x acceleration. a) Graph of produced Z-spectrum points for septal region of the heart, and overall Lorentzian-line-fits. b) Zero-filled IFFT image reconstruction of 2x subsampled acquisitions where missing k-space has been zero-filled. c) Multiscale low rank reconstruction of these same acquisitions.

Figure 3. Example reconstruction results for 4x acceleration. a) Graph of produced Z-spectrum points and respective Lorentzian-line-fits. b) Zero-filled IFFT reconstruction of 4x subsampled and zero-filled acquisitions. c) MSLR reconstruction of these same acquisitions. Note faithful reconstruction of RF banding.

Figure 4. Example reconstruction results for 8x acceleration. a) Graph of produced Z-spectrum points and respective Lorentzian-line-fits. b) Zero-filled IFFT reconstruction of 8x subsampled and zero-filled acquisitions. c) MSLR reconstruction of these same acquisitions. Note the appearance of high-frequency reconstruction artifacts.

Figure 5. Loss graphs for MSLR and IFFT reconstructions, averaged over 10 acquired scans. Individual scan loss is calculated by $$$log_2(\frac{P_{recon}}{P_{fs}})$$$ where $$$P_{recon}$$$ are Lorentzian-line-fit parameters for the reconstructed scans, and $$$P_{fs}$$$ are those for the corresponding fully sampled scan. Losses are separated into graphs for the 3 Lorentzian parameters and 4 pools of interest. Amplitude measurements for each scan are normalized by their respective water pool amplitudes.