A flexible approach for fat-water separation with bipolar readouts and correction of gradient-induced phase and amplitude effects

Purpose: To develop a fat-water separation approach that corrects bipolar readout gradient induced effects, without additional scans, that is compatible with any fat-water separation method. Theory and Methods: The proposed approach combines joint fat-water separation of the odd and even echoes of a bipolar multi-echo gradient echo acquisition with an inverse problem to find least-squares estimates for phase and amplitude corrections to eliminate bipolar-induced effects. Optimization of sequence parameter selection through the calculation of the number of signal averages (NSA) with Cram\'er-Rao Bound theory (CRB) is presented. The application of the proposed approach is demonstrated with a graph cut optimization and further characterization of the accuracy was performed via Monte Carlo Simulations (MC). The proposed approach was tested in phantoms and in vivo. Proton density fat fraction maps (PDFF) were evaluated to quantify performance. Results: NSA calculations suggest short TE1 and {\Delta}TE=1.5 ms as optimal alternatives for fat-water separation. MC simulations demonstrated accurate estimation of fat and water complex signals, {\psi}, and R_2^* with mean relative error within 1%. In phantoms and in vivo, the proposed approach effectively eliminated effects induced by bipolar readout gradients, improving the outcome of the fat-water separation. Conclusion: We proposed an approach to correct bipolar readout-induced effects that are detrimental for fat-water separation. This approach can extend the use of existing fat-water separation techniques designed for data acquired using unipolar readout gradients to data collected with bipolar readout gradients.