Spatial RF Pulse Design in Local Rotating Frame

Seung-Kyun Lee¹

In magnetic resonance, a gradient- and voxel-dependent rotating frame, which we call a local rotating frame can eliminate all longitudinal magnetic fields in magnetization dynamics and therefore significantly simplifies the theory and practice of spatial RF pulse design. When the gradient waveform is pre-determined, as is the case in most existing numerical RF design methods, the frame transformation is completely straightforward, and removes need for repeated calculation of the same gradient effects as RF pulse is iteratively updated. After introducing basic theoretical elements of the new frame approach, we demonstrate its usefulness in two examples. First, we demonstrate calculation of the residual dephasing in slice selective excitation caused by nonlinearity of the Bloch equations by analytical integration of the equations in the local rotating frame. Second, we show that numerical integration of the Bloch equations is made significantly faster in the new frame due to the lack of strong longitudinal field. We discuss the relevance of the new approach in the context of iterative RF design in parallel transmit.