Nonlinear parameter estimation with physics-constrained spectral–spatial priors for highly accelerated chemical exchange saturation transfer MRI

<i>Objective.</i>To develop a nonlinear, model-based parameter estimation method directly from incomplete measurements in<i>k</i> - <i>w</i>space for robust spectral analysis in highly accelerated chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI).<i>Approach</i>. A CEST-specific, separable nonlinear model, which describes spectral decomposition using multi-pool Lorentzian functions (conventional magnetization transfer (MT), direct saturation of water signals (DS), amide, amine, and nuclear Overhauser effect) derived from the steady-state Bloch McConnel equation, is incorporated into a measurement model in CEST MRI. Furthermore, signal drop in saturation transfer experiments is formulated by an additional, separable nonlinear spectral prior indicating that the symmetric z-spectra synthesized using conventional MT and DS always remain higher or equal to the whole z-spectra with all pools. Given the above considerations, linear and nonlinear parameters in the proposed method are estimated in an alternating fashion directly from highly incomplete measurements in<i>k</i> - <i>w</i>space by solving a constrained optimization problem with the physics-constrained spectral priors while imposing additional sparsity priors on spatial parameter maps.<i>Main results.</i>Compared with conventional methods, the proposed method yields clearer delineation of tumor-specific CEST maps without apparent artifact and noise.<i>Significance.</i>We successfully demonstrated the feasibility of the proposed method for CEST MRI with highly incomplete measurements thus enabling high-resolution whole brain CEST MRI in clinically reasonable imaging time.