Introducing a new, model-based Extraction of z-spectrum Asymmetry using SYmmetric basis (EASY) that directly characterizes the signal sources of the asymmetric z-spectrum.Chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI) [1,2] is an indirect molecular imaging technique, in which a small molecular signal is amplified by chemical exchange phenomenon. Multiple acquisition of imaging data with varying saturation frequencies, called z-spectrum acquisition, is typically performed [2], and then subtraction-based MTR asymmetry analysis is employed to investigate the effect of CEST on MRI. However, since the z-spectrum is additionally convoluted by inherent asymmetric MT, nuclear Overhauser enhancement (NOE), etc, conventional asymmetry analysis is prone to substantial errors. To tackle these problems, in this work we introduce a new, model-based extraction method of the z-spectrum asymmetry using symmetric basis (EASY) to directly characterize the signal sources of the asymmetric z-spectrum.

The CEST z-spectrum, if main magnetic field inhomogeneities are corrected, includes symmetric modulation of water signal with respect to the resonance frequency of water due to direct saturation and symmetric MT effects, while pertaining asymmetric properties due to inherently asymmetric MT, NOE, and CEST effects. Given the considerations above, in this work we propose a new, spatiotemporal signal model in the B₀-corrected z-spectrum: $$$\mathrm{S = S_{sym} + S_{asym} + N}$$$, 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. Nevertheless, the proposed signal decomposition model is highly underdetermined, and both components are possibly inter-related. To tackle these problems, the proposed, z-spectrum decomposition is performed by solving a constrained optimization problem with the following priors: 1) the symmetric z-spectrum can be modelled by a product of spatial coefficients (U) and temporal (V) basis ($$$\mathrm{S_{sym} = UV}$$$), and the temporal basis can be pre-determined using the Bloch simulation based z-spectra by taking only symmetric signal pools into account, 2) the asymmetric z-spectrum has high spatiotemporal correlation ($$$\mathrm{||S_{asym}||_*}$$$), and 3) signal pools, which generate the asymmetric z-spectrum, always result in an additional signal decrease in water (S_asym<0). Thus, the proposed spectrum decomposition problem is written by:

$$\mathrm{\min_{S_{sym}, S_{asym}} ||S – (S_{sym}+S_{asym})||_2^2 + λ_L||S_{asym}||_* \\ \text{ subject to } \quad S_{sym}=UV, S_{asym}<0.}$$

Numerical simulations and experimental studies in creatine-agar phantom and brain were performed on 3T (Siemens Trio) using the proposed method and conventional MTR asymmetry analysis (MTR_asym(S,f)= S(-f)/S₀ - S(f)/S₀) for comparison. S₀ is the reference image without CEST preparation. S, S_sym, S_asym, MTR_asym(S), and MTR_asym(S_asym) were estimated. Furthermore, the proposed, EASY asymmetry analysis was performed in brain by varying the amplitude of CEST saturation pulses. Imaging parameters were described in the caption of the corresponding figures.

Figures 2 and 3 represent S, S_sym, S_asym, MTR_asym(S), and MTR_asym(S_asym) in numerical simulation and creatine-agar phantom, respectively. Conventional MTR_asym(S), and MTR_asym(S_asym), and S_asym are nearly identical in both simulation and phantom studies except the sign change in S_asym, because CEST is the only asymmetric component in the z-spectrum. However, conventional MTR_asym(S) and S_asym in brain exhibit discrepancies possibly due to additional, asymmetric signal contributions from inherent MT and NOE, etc, in which the former cannot differentiate CEST from non-CEST and thus results in mixed asymmetry between them (Fig. 4). Figure 5 demonstrates that S_asym in the proposed EASY method is highly sensitive to varying amplitudes of saturating RF pulses at 3.5 ppm (amide proton pool) and 2.0 ppm (amine proton pool). It is noted that CEST effects increases with rising amplitude of saturating RF pulses.We successfully demonstrated the feasibility of the proposed, EASY asymmetry analysis in numerical simulation, creatine-agar phantom, and in vivo brain. It is expected that the proposed EASY method enables signal separation of CEST, inherent asymmetric MT, and NOE in the z-spectrum, though its utility in in vivo is to be further investigated in the future.