Spatial RF Pulse Design in Local Rotating Frame

Introduction Formulation of spatial RF pulse design in a gradient-dependent rotating frame is introduced. This work was motivated by the need for a fast RF design algorithm for use in a high-field parallel transmit system where dielectric effect creates transmit field distribution with significant patientdependent variability. The new reference frame, called a “local rotating frame”, transforms away any (known) longitudinal magnetic fields present in the problem, and thereby greatly simplifies analytical and numerical calculations of spatial RF pulse response in a single-coil or a parallel transmit system. We demonstrate the application of the new method in analytical and numerical solutions of the Bloch equations in the spinor domain. Theory and Methods Conventionally, spin dynamics in MRI is formulated in a frame rotating at a fixed Larmor frequency determined by the static field. We define a local rotating frame as a frame which has an additional transverse phase –φ (r, t) with respect to the conventional frame, where φ (r, t) = ( ) ∫ ⋅ + t dt t B 0 0 ' ) ' ( ) ( r G r δ γ . Here δB0(r) and G(t) are off-resonance field and applied gradient field,