Introducing a new, model-based direct Extraction method of the z-spectrum Asymmetry from undersampled k-space using SYmmetric basis (k-EASY), which is a compressed sensing approach to accelerate z-spectrum acquisition while directly characterizing the signal sources of the asymmetric z-spectrum.In chemical exchange saturation transfer (CEST) MRI[1], multiple acquisition of imaging data with varying saturation frequencies is typically performed[2], which prohibitively prolongs imaging time. Furthermore, conventional, subtraction-based MTR asymmetry analysis is prone to substantial errors, because the z-spectrum is convoluted by CEST as well as inherent asymmetric MT, nuclear Overhauser enhancement (NOE), etc. To tackle these problems, in this work we propose a new, model-based direct Extraction of the z-spectrum Asymmetry from undersampled k-space using SYmmetric basis (k-EASY) that incorporates main field inhomogeneity correction and z-spectrum asymmetry analysis into a framework of compressed sensing.

The z-spectrum in CEST MRI consists of symmetric signal modulation with respect to the resonance frequency of water due to direct water saturation and symmetric MT as well as asymmetric signal modulation due to inherent asymmetric MT, NOE, and CEST, etc. In this work, we propose a new, z-spectrum signal model consisting of symmetric and asymmetric components under the assumption that main field inhomogeneities are corrected in the z-spectral direction: $$$\mathrm{S=S_{sym}+S_{asym}+N}$$$, where S is a Casorati matrix of the total z-spectrum signal, S_sym is the symmetric component, S_asym is the asymmetric component, and N is additive noise. Since the aforementioned signal model is highly underdetermined and S_sym and S_asym are somewhat correlated, the proposed z-spectrum decomposition in undersampled k-space is performed by solving a constrained optimization problem with the following priors: 1)S_sym is modeled by a product of spatial coefficients (U) and temporal (V) basis (S_sym=UV), and the temporal basis can be determined using the Bloch simulation model with only symmetric signal pools taken into account, 2)the spatial coefficients are sparse in a transform domain, 3) S_asym is highly spatiotemporally correlated($$$\mathrm{||S_{asym}||_*}$$$), and 4) S_asym results in an additional signal drop (saturation) in S ($$$\mathrm{S_{asym}<0}$$$). Given the considerations above, the proposed z-spectrum decomposition in k-space is described by the following optimization problem:

$$\mathrm{\min_{S_{sym},S_{asym}}||d – F_u(φ(S_{sym}+S_{asym}))||_2^2+λ_S||ψ(U)||_1+λ_L||S_{asym}||_* \\ \text{subject to} \quad S_{sym}=UV, S_{asym}<0,}$$

where d is the measured data in k-space, φ represents the two-step operator, phase modulation in the in-plane followed by B₀ magnetic field modulation in the z-spectral direction, F_u is the undersampled Fourier transform, and ψ is the sparsifying transform. It is assumed that phase modulation in the z-spectral direction remains identical. Image phase and B₀ magnetic field are used as prior information. Discrete wavelet transform is used as a sparsifying operator, and spline interpolator is used as B₀ field modulation operator. Symmetric basis, V, is extracted from 10000 simulated z-spectra with only symmetric components taken into account (Fig.1), and seven basis functions are then employed.

Experimental studies in creatine-agar phantom and brain were performed on 3T (Siemens Trio), and imaging parameters were described in the caption of the corresponding figures.

Figure 2 demonstrates proposed method can generate same contrast when it is compared with conventional MTR asymmetry analysis. Because there is no confounding asymmetry component of frequency of interest, 2.0ppm in creatine-agar phantom, extracted asymmetry of z-spectrum using proposed method, -S_asym, MTR asymmetry analysis of the extracted asymmetry, MTR_asym(S_asym), and MTR asymmetry analysis of B0-corrected z-spectrum, MTR_asym(S), result in similar images. Especially, extracted asymmetry shows pure CEST effect of target frequency and comparison of MTR asymmetry analysis of the extracted asymmetry and B0-corrected z-spectrum shows accuracy of reconstruction algorithm qualitatively. In creatine-agar phantom, proposed method work properly even in high reduction factor (R=6). Figure 3 demonstrates proposed method can separate out sources of conventional MTR asymmetry analysis from undersampled CEST data. Especially in in-vivo CEST experiments, there is confounding asymmetry effect on z-spectrum and it generates error in MTR asymmetry analysis. According to the results of proposed method, in the experiment setting, there is almost zero CEST effect at 3.5ppm and there is large NOE or asymmetric MT effect at -3.5ppm, and it generates contrast of conventional MTR asymmetry analysis. Figure 4 demonstrates that S_asym in the proposed k-EASY method is highly sensitive to varying amplitudes of saturating RF pulses.

We successfully demonstrated that the proposed k-EASY method, which incorporates a novel z-spectrum asymmetric analysis (EASY) into a framework of compressed sensing, not only produces signal separation of CEST, inherent asymmetric MT, and NOE directly from undersampled k-space but also makes it possible to achieve high acceleration without apparent artifact and amplified noise, though its utility in in vivo is to be further investigated in the future.