A hybrid numeric-analytic solution for pulsed CEST

Chemical exchange saturation transfer (CEST) methods measure the effect of magnetization exchange between solutes and water. While CEST methods are often implemented using a train of off-resonant shaped RF pulses, they are typically analyzed as if the irradiation were continuous. This approximation does not account for exchange of rotated magnetization, unique to pulsed irradiation and exploited by chemical exchange rotation transfer methods. In this work, we derive and test an analytic solution for the steady-state water signal under pulsed irradiation by extending a previous work to include the effects of pulse shape. The solution is largely accurate at all offsets, but this accuracy diminishes at higher exchange rates and when applying pulse shapes with large root-mean-squared to mean ratios (such as multi-lobe sinc pulses).